Welcome!

You have some basic info down well, I think. I'll offer my own advice, but please be aware that the final decision comes down to your personal preferred play style. One thing I will stress: "major skills" does not mean "skills most used by the character." That is a very misleading assumption that is often made. It CAN mean that, but using such a definition means creating and developing your character accordingly. For my play style, I view "major skills" as meaning "needs special courses, training, practice sessions, etc in order to be developed." In other words, such skills (for my play style) are ones that are developed outside of normal daily activities, not as part of my character's usual actions. This allows me freedom to use my normally used skills as I wish, more or less, or at least much more freely than if the commonly used skills were majors. It is a valid explanation within the game world, too, so it doesn't break immersion or character concept.
As an additional note before I offer any advice... ultimately, the game allows you to counter any problems you may have in various ways through enchanted items, magic spells, potions, etc. This is especially true on normal difficulty level (which I assume you are using for now).
Regarding Heavy Armor... yes, I would use it as a major rather than Block simply because it is even easier to avoid using than Block. Also, it fits your concept as far as avoiding it. This logic leads into...
... Sneak should not be a major skill, especially for a stealth character. The last thing you want is to be faced with a choice between sneaking and leveling versus not sneaking and being caught, or simply being out of character concept. Security would be a far better choice (again, you can easily control using or not using Security). Marksman is possible if you use a bow, but it can create problems if you plan to rely on it as a primary offense (again, uncontrolled leveling).
Speed skill: Light Armor. Easy choice since the other two are almost certainly needed simply for movement. Easy to control too... simply don't use it, or only use it when you choose to train it or need to use it for some reason. There are plenty of alternatives to armor, though, particulary enchanted clothing, jewelry, and potions/spells. Also, note that wearing ANY kind of armor causes a decrease in spell effectiveness. Since you mentioned that your character will use appropriate magic, the choice to avoid using armor under most circumstances may be even more important.
For Strength major skill, choose whatever you will NOT use. You list Blade, so I assume you plan to use Blunt weapons (or bow, perhaps). If not, then put Blunt as major (if you plan to use Blade weapons).
Alteration is the best Willpower major. NOTE: Restoration is an incredible school for offensive magic, so do not assume that it is only there for healing! Many people make that mistake. It levels slowly, but that's because of the fact that using it properly tends to mean that you will use it A LOT. For example, buffs to skills and stats are under Restoration. You want 100 in a skill for a couple of seconds to do something? Restoration will do that for you. Want to carry a load out of a cave? Repeatedly casting Restoration buffs will do that, too.
Learn the nature of spell chaining. Also, learn about proper spell stacking. Spell chaining is most important, but spell stacking is also good even for a character such as yours.
You may want to consider making Magic your specialization rather than Stealth. This evens out the bonuses to using skills, somewhat. It's up to you, though.
I'd stick with Mysticism for major Intelligence skill. Alchemy levels very fast, anyway, and you would probably run into the usual uncontrolled leveling issue with Alchemy as a major (unless you avoid potions, of course). There are not many spells under Mysticism that you will use, and certainly not regularly. The two most used aree probably Detect Life and Soul Trap. Pretty easy to control using them, especially if you consider potions and enchanted items. If someone on the wiki is saying that Mysticism falls under uncontrolled leveling, I'd say that this is a mistake and should be corrected.
MOST IMPORTANT: Do not have Illusion as a major skill for stealth characters! Use Speechcraft as it is much easier to control. Illusion levels very quickly, like most magic schools, and stealth characters will almost certainly want to use many of the spells in it, especially after it hits Journeyman (i.e., level 50). Illusion is actuallly very overpowered and you may discover that you need to avoid using it or it takes a lot of enjoyment out of the game. It depends on what you enjoy, though... this is just what happens for some people.