I'm an obsessive Witcher fan and only paused my 6th playthrough of The Witcher 2 on 11/10/11 (for obvious reasons). A build true to Geralt would probably be a Nord, that character design looks good. As for skills/personality...
-Level Two-Handed as fast as possible. Get all the good perks. Geralt would not limit himself to the 'silver greatsword', he would easily use an enchanted Ebony greatsword, not that different from the Sword of the Dun Banner or D'Yaebl. Sure, he is supposed to have two swords, but that's more of a gameplay mechanic since monsters and men die equally in Skyrim.
-Light armor for sure. Always wear some light jackboots of some sort - and Geralt would never equip glass armor, doesn't match his visual style. The rest of the light armor is probably okay. Geralt would retain light gloves throughout, and would certainly wear rings and amulets. Only hoods for headgear though!
-Get the spell for Night-Eye and use it often, Geralt has a mutant's night vision.
-Geralt's magic are the five signs, simple magic tricks which he can improve to very, very powerful levels. Igni is best represented by powerlevelling Destruction, Firebolt, Fireball, Flames, Incinerate are all okay. Yrden is a magical trap - a lightning rune is most accurate. Axii is mind control - command daedra, agent of subterfuge, or any other comparable allegiance altering spell is legal. Aard is a force push/blast - Fus Ro Dah suffices. And Quen would be a lightning shield spell. MAYBE oakflesh line of spells but that is iffy. NOT Wards, that would be for Triss.
Nope. Every sorceror in the books and games laughs at people referring to Witcher's signs as real magic - they're considered little more than cheap tricks, and are used by witchers specifically because they require an absolutely minimal magical aptitude. They also CAN use wards in the sense of the heliotrop sign in the books, which blocks spells. Also, Axii only calms people, it's not mind control.
-Alchemy constantly, potions for every occasion. Geralt does not use poisons but I wouldn't say it is beyond the realm of possibility, given that there are no bombs in Skyrim.
False. Geralt uses poisonous blade oils with the intention of creating additional injury to monsters and humans alike. He also uses a potion known as 'black blood' which harms haemophages is they happen to bite the witcher.
-Take no followers, Geralt works alone.
-Avoid Mage's Guild completely. Could do some work for the Thieves' Guild. Companions okay up until they ask you to become a Werewolf, a big no-no. Geralt inevitably gets dragged into national conflicts (Witcher 2, it's unavoidable) and would side with whoever you believe in more. Geralt would probably lean more towards the stability of the Legion and the Empire, they resemble Temeria more than the Stormcloaks.
Ideally Geralt wouldn't side with anyone, in the books he remains neutral at all times whenever possible.
-Daedra are from other dimensions and Geralt hates stuff from other dimensions. The Wild Hunt is from a parallel dimension and are the cause of all his memory loss, troubles and issues. Butcher Daedra worshippers, mess up their plans and kill them wherever possible.
Lolwut? You're having a laugh. He follows the wild hunt because they took Yennefer, he doesn't hate all things from other worlds by any means.
However, the more benevolent ones (The Break of Dawn, Azura's Star) are okay. And Sanguine's is definitely legal, given there is a similar quest in Witcher 2, "Hung Over".
-Hunt down vampires with a passion. And amateur spellcasters are fodder for Geralt.
-Bounties, bounties, bounties. Do them again and again, this is the Witcher's pride and joy.
-The Dark Brotherhood are Assassins of Kings. The Witcher 2 pits Geralt against the Assassins of Kings. It should be pretty clear that Astrid must not leave the Abandoned shack alive, and the Dark Brotherhood must be purged ASAP.
-Geralt could do a little thievery but is not a common thief. He will sneak when he has to but prefers a straight fight and would not pickpocket.
-However, Geralt happily takes peoples' stuff from their homes at random.
I don't know where you're getting most of this from. Geralt especially has a big thing against killing people for money. At best he would hunt dragons, which as sapient creatures are a grey area and generally only huntable if evil (as they are in Skyrim) Geralt is also entirely capable and well suited to stealth due to his augmented abilities as a witcher; they see well in the dark and are known to be able to get around silently.
-Geralt is generally law abiding, but if it is urgent guards are merely pawns to be chopped down. However, if Geralt starts getting hit with guard's arrows, he would yield (as arrows = cutscene death in Witcher 2 with lawbreaking).
-Geralt would not draw his sword in a populated area unless there was an attack by monster or man.
-Geralt is a crafter and would not hesitate to use the grindstone, smelter, forge and tanning rack.
Geralt IIRC is not a crafter at all, he makes potions and bombs, but has to pay others to make weapons, armour and traps for him.
-Geralt would harvest any alchemical ingredient from the corpse of a monster and leave the rest, unless the pelts or trophies would bring solid cash.
-The Witcher is not a man who settles in one place. Avoid buying a house. If this cannot be avoided, get the cheap house in Whiterun. Also, make sure if you must have a follower, she is attractive, female, and married to you if possible. Human preferred but Geralt is not picky, an elf race will do. Spellcaster preferred, and make sure she wields a staff of fireballs.
-Fetch quests are okay, Geralt is of superhuman endurance and used to backtracking. Resolving any relationships disputes is out of the question, however, as he makes quite clear in Vergen in Chapter 2 of The Witcher 2. A Witcher is, self-described by Geralt, a "Problem Solver". For monstrous, magical and mythic missions.
-Geralt does not hesitate to kill any human in cold blood if it is crucial to his mission or they challenge him. Bandits are of special priority, Geralt will elegantly butcher highwaymen, thugs and brigands to clean the streets and forest alike.
-Ghosts, Skeletons and Draugr are the closest enemies resembling the Wild Hunt, Geralt's ultimate nemeses. Butcher them with special fury and root out every tomb you find. Dragon Priests in particular are enemies Geralt would hold hatred for, as with the application of Witcher lore they would be the spectrally possessed avatars of the evil elves of the Wild Hunt.
-Speaking of Elves, the Thalmor are utterly foreign to Skyrim like the Wild Hunt Elves are foreign to Temeria. Both have agendas of slavery and domination. Butcher the Thalmor.
Again, this is a bit off. Geralt wouldn't go out of his way to kill any humans who aren't about to kill him or somebody else. He doesn't just go around clearing the forests of bandits.
and again, he is chasing the wild hunt for a specific reason, if he got Yennefer back he wouldn't give a [censored] about them at all. At the end of TW2 he's done with the Wild hunt despite only killing some of them, he just wants Yennefer.