As we know, the Empire is planning a secret attack on the Dominion during the events of Skyrim. Once the Empire turns on them where would the Dominion's primary route into Skyrim be? Where would they try to invade from? The only routes I know of would be thus:

Hammerfell: The most direct route. However, from what I've read they already had their butts handed to them by the Redguard once before. Also, don't they have a treaty with them as a result of the tanning they received? If so, that route is out of the question.

Cyrodiil: This is where the Imperial forces are massing, so they'd have one hell of a fight on their hands before they even reached Skyrim.

Valenwood/Elsweyr: Both vulnerable to interception by the massed Imperial forces.

Morrowind: One hell of a journey, but the pass into the Rift seems pretty easily traversed.

That leaves the route by sea around the western side of the continent and into the Sea of Ghosts, maybe landing on the coast near Dawnstar?

Your statement makes several assumptions, but I'll answer a few.

They did not get their butts handed to them in Hammerfell. They took over half the province and then reached a stalemate. They both signed a treaty and the Dominion withdrew.

It could be possible to maintain a supply line through Cryodil. The Battle of the Red Ring devastated both sides which is why the Imperials signed the WGC. You're assuming the Empire will turn on the Dominion before the Dominion is ready to invade (which honestly, I don't think their plan is to invade Skyrim). There is a reason why the Dominion is trying to prolong the Civil War, to make Skyrim a non-factor when the time comes to attack Cyrodil or when Cyrodil declares war it's brethren to the North are too busy with themselves and their dwindling and split forces can't come south to help.

Neither are even a route to Skyrim.

Morrowind is the long way around, and I doubt they would be helpful to the Aldmeri forces unless they are coaxed to join (and with the Thalmor in power, that chance is slim to none...they would need to fall and another government rise to take their place).

Sailing around might be the best option. The Altmer have the strongest navy. Granted the Redguard and Nords are excellent sailors, when it comes to military force on the blue, Altmer rules the waves. As a person who understands the importance of blue water dominance, it really increases your mobility and options. Sure it might be the long way around as the crow flies, but ships can sail faster, farther, and longer than an army can march.

Again though, you're assuming they want to take over Skyrim right now. Skyrim doesn't have as much strategic value as Cyrodil does, unless you get Morrowind to join the AD (again, Thalmor need to be removed from power, which I really hope they do regardless...would make for a much better Dominion). If the Dunmer join up with their Mer-brethren, then they could effectilvey squash the Empire from both sides and if not take over all of Cyrodil, take over almost half of it. Then again, these wars are fought for Thalmor ideals and goals. If they are overthrown, who knows what the next desire of the Dominion will be (we could safely assume though, it's never to rejoin the Empire)

I'm saying in the event of the Empire attacking them. I would have expected them to make a grab for Skyrim whilst the majority of their forces are engaged with the Imperial Legion in the south. Not only would they have Skyrim under their control, but they could open a second front on Cyrodiil from the north.

They could move forces into Cyrodiil through Valenwood or Elsweyr. But as I said, that would allow the bulk of the Imperial Legion to intercept them.

And I'm guessing that moving forces through Hammerfell into Skyrim would probably break the treaty and cause another war with the Redguard, which I think would be the last thing they'd want, at least for the time being.

Yes but would it really be worth it?

First they would have to sail their fleet all the way around Tamriel. They could go the fast way up past Hammerfell and by High Rock, but then they would have to deal with the navies of Hammerfell and the Empire. And even if they cannot defeat the combined naval forces of the Dominion, they could still proved a nusciance to the Dominion's supply lines. If they go the long way past Black Marsh and Morrowind, they would have less to worry about from Imperial navies, they would still have to deal with raiders attacking their supply lines (Reavers and the like).

Then when they get to Skyrim they will have a lot of land to cover. They may be able to take the major ports (Solitude, Dawnstar, and Windhelm), but they would still need to take the interior. This would be easier said than done, because in addition to local armed forces, be they Imperial, Stormcloak, or both, they will have to deal with an incredible belligerent populace. Sure, the Nords are divided between Imperial supporters and Stormcloak supporters, but throughout history the Nords have always been willing to put aside their differences to kill some elves, and if an overly powerful invading force takes over, especially one made out of elves, they are liable to go Guerilla.

Essentially they would want to avoid the Reach, Hjaalmarch, the Pale, Winterhold, and the more volcanic parts of Eastmarch, as these are all places where it will be very easy for a local force to attack from. The Reach because of its mountains, cliffs, and winding roads, not to mention the existence of another set of belligerent Guerilla's (the Forsworn). Hjaalmarch is a misty, dark, swamp. The Pale and Winterhold are both incredible cold, which is something that the tropical Altmer, Bosmer, and Khajiit will have trouble dealing with, even with mitigating magic. And the Eastmarch is filled with caves and hiding spots. So the Dominion would not want to take over all of Skyrim. They would want to concentrate their forces on Solitude, Whiterun, and parts of Falkreath hold, forming a supply line down to Pale Pass. And as for Pale Pass, as said before the Dominion forces will probably have trouble dealing with the cold, and since Pale Pass is not that wide a space, the Imperials could easily bottleneck any Dominion forces attempting to go through it. And if while doing all this the Dominion forces lose their grip on whatever ports they are holding, then they will be stuck in a foreign, cold, and unfamiliar land with no hope of rescue, surrounded by angry Nords, many of whom would love to take some elf heads.

Ultimately it would be a better use of the Dominion's forces to focus on attacking Cyrodiil directly.

We don't really know what the Dominions military might is at the moment either. Oh sure, the Thalmor are skilled enough to go on par with the Blades, but the actual boots on the ground is a different matter. For what its worth, Elenwen's messages imply that the Dominions resources are being strained trying to enforce the WGC. Given that they didn't originally have a presence in Talos-capital-of-the-Empire Skyrim, its possible they didn't intend to be there in the first place.

Strikes me that their losses at White-Gold were significant to the point of having to give up the ghost of direct conquest. My gut feeling is that the Dominion is puffing up its chest to make it look bigger then it really is, and for all their machinations, are not in a good position to actually rally an effective conquest on anyone for the time being, let alone as some place as far removed as Skyrim. Unless Cyrodiil gives them the okay to march large swaths of troops through their land, which is pretty unlikely in of itself, I don't see them being able to wage any war up north efficiently.

Seems like a strange assumption myself. If the strength of your enemy is directly attacking your territory, why would you perform such a incredibly wide and risky flank manuever when only a small one is needed? If France was the Dominion, and Germany was Cyrodiil, then you'd be suggesting to France to take valuable manpower to sail around Denmark to invade Poland in order to open up a second front. If your force manages to get past all the hostile navies from Germany, Denmark, and Poland, and if you still somehow maintained the element of surprise, you'd land an army with little chance of being resupplied. And this isn't even near the distances you'd find in Tamriel. Though you'd have magic o'course.

The Dominion, in essence, would be performing a Hannibal but your its territories aren't protected by the Meditteranean Sea and Carthage would already be calling you back before you even reached Italy because Roman armies roaming around Africa and threatening the capital.

Point being, Skyrim is anything but a soft target. They share a really wide border with the Empire, and probably wouldn't have the manpower to commit elsewhere. And if they did, it would be a lot less risky to sail a force up the Niben or invade southern Hammerfell and attack across the Brena (though that would drag Hammerfell into the conflict - not a worthwhile endeavor).