One-handed Skill to legendary?

Legendary status was implemented to allow resetting skills. Side effects of this was that you could level above level 81.

In Skyrim some enemies scale with your level while others do not. Wolves for example will stay weak the whole game while higher tier enemies will be 'difficult' the entire game.

Before resetting your main skill you should test out how strong the difference is. Just save the game and do a dungeon or two.

You will loose all benefits of this skill tree, meaning damage will drop, special attacks are missing.

If you manage to play this way you will be rewarded however. As you use one handed anyway you will level it without really noticing. Also you will gain extra experience from these level ups meaning you increase you total level resulting in more stats and skill points.

Yes, your damage will become that of a perkless level 15 one-handed character, about the strength of a new character. Your existing one-handed perks will be refunded and can be reallocated.

But doing it or not depends on your survivability after making one-handed legendary. I will suggest doing so since one-handed will your primary combat style, you will find yourself levelling quickly once you reset. But you might potentially find yourself overwhelmed after the reduction in damage so you might want to prepare some extra potions and strengthen your Armour skills before doing so.

Avoiding it entirely only slows your future levelling speed so if you prefer a more relaxing play it is perfectly fine too.

Yes and yes, as explained in other answers.

Despite these rather serious drawbacks, resetting a primary combat skill is very feasible for most character builds. You will probably want to lean on other skills in order to make up for the reduction in damage (but take care that you do not stop using one handed altogether, or you'll never level it back up again!). Here are some suggestions, starting with the ones most likely to match the specific build (assassin) you have described:

• Be very good at backstabbing. Have the relevant sneak perks maxed and a high-quality dagger. This also has the advantage that it will directly level one handed.
• Have good archery, sneak, and (optionally) alchemy skills, and focus on ranged sneak attacks. Use invisibility potions to "reset" your stealth after each attack, or use paralysis poisons to incapacitate enemies so that you can kill them more easily. You can easily pick off nearly an entire dungeon this way. Any character will almost certainly have at least halfway decent archery because of all the dragons.
• Have good equipment which does a substantial amount of base damage by itself.
• Have good armor skills. Be at the armor cap.
• Be good at dealing a lot of damage with destruction or conjuration magic. It's also a Good Idea to level the other three schools of magic, but they're a bit more situational. Illusion in particular may be useful for a stealth-oriented character (muffle and invisibility, plus all the AI manipulation spells).
• Have strong followers. This dovetails nicely with conjuration. Prefer followers and summons who use a different style of fighting from you. Followers and summons can complicate the use of sneak, but they can also work with it. Tank characters like Lydia are good at drawing the enemy's attention and allowing you to get in lots of ranged attacks.

Finally, a parting word of advice: Go slowly. Do not (for example) make archery, one/two handed, and light/heavy armor legendary all at once. Make one of them legendary, wait for it to recover to a viable level, and then make a different one legendary. Always save before making a skill legendary, and back out to the save if you find it too hard to continue your game.