I mean one hit with a knife or sword rarely kills instantly or an arrow either for that matter.
Killing immediately wouldn't be necessary. The point would be for one strike to be able to kill you... even if it takes a while.
Can you make it precise enough that the "one hit kill" isn't dependent on "roll dice to see if the hit bypasses defenses" ?
My idea would be to make the the success/failure of a strike based MOSTLY upon what weapon is used against what armor. However, I do see adding a "dice roll" to the equation in a limited role. Basically, an iron dagger strike would ALWAYS succeed on an unarmored/unblocking target. It would NEVER succeed against a target wearing Daedric armor. It may receive a high chance to succeed against leather armor, while receiving a low chance to succeed against steel armor. A Daedric battleaxe strike would pretty much always be successful against anything really save for ebony, Daedric, or dragon. On those, there would at least be a decent chance of protecting against such a strike, though it may still be low.
Also, the only reason why I wouldn't use this is because of fatality/finisher moves.
I would prefer to set every weapon's "damage stat" to 0. All damage should be implemented through actual damage enchantments such as bleeding. I may be mistaken, but wouldn't that minimize the finishing moves?
I think adding bleed damage instead of one hit kill might work better. Or bleed damage on top of critical damage.
Indeed. I'm already experimenting with bleeding damage. Seems to be working quite well. Shouldn't be much need for anything else.
- Shields block all damage, all the time (excluding arrows and magic)
Yes, blocking should virtually offer complete protection from melee strikes (heavy weapons may still break through). I would think that shields should block arrows also. I would hope that shields could also block a lot of magic, but that's another issue altogether

The thing is though that a lot of the 1-hit mods turn games into sniper/ranged fests. I can tell you right now the only way you will live in such a world is to learn to use a bow and sneak well.
That's true. But it's a double-edged sword. NPC archers will be just as lethal as you are. And an arrow most likely will not drop an enemy immediately like in the movies. So be ready for very angry NPC's that you just shot to be charging as fast as they are able to. Not to mention that you're usually going to be fighting multiple enemies, so you'd better be fast if you rely solely on a bow.
I do figure it will take a lot longer to bleed out from an arrow than it would for a sword slash, so you'll want to hit each target with multiple arrows. We need to get the whole "Boromir's Last Stand" vibe going

If the swing is interrupted by a bash or blocked by a shield then the combat would continue. Only clean hits would mean 'dead'.
That is exactly the case. "Defense wins championships." Imagine Skyrim to play like Ninja Gaiden. It's MUCH more important to avoid getting hit than to actually hit the enemy.
Also, a "clean" hit would mean a successful strike. Just because a target may be completely unaware of an attacker, his armor is still in effect. A weapon must break through the armor for a strike to be successful. Again, an iron dagger will NEVER break through Daedric armor no matter how solid the blow.