Hide
Feedback: An assassin without stealth isn't an assassin, just an idiot with two daggers.
Suggestion:Reusable during combat; Casting time 2sec; damage stops it; automatic critical hit on next strike; additional crit. damage per extra level; constant 40% speed malus. +50% dodge rate while hidden.
Comment: I bet you didn't saw that coming! Yes, I suggest to make hide usable during combat.
Whereas most of the other finisher skills get an extra bonus on certain conditions of the target (stunned, knocked down, frozen), the assassin should get this from hide, not from a stupid/random 'Mark of Shadow'. Except for the highest damaging skills, the addional damage bonus is 'eaten up' by the casting time and 2sec are still enough for opponents to react.
In PvE it would be the same as if your opponents are 'neutral' by default.
This would be pretty amazing, can't lie, but resetting hide also one of the key features of the Rogue class that makes it unique (Smoke Bomb).
Come to think of it, the rogue class actually seems to have more of the traditional sin characteristics (agi = +2 dodge, vs sin's +1, for example, and reusable hide); they're the hide+dodge class, and sin the run+stun. Your suggestions, while valid, would probably muddy this distinction up somewhat, since they are more geared towards hide+dodge, and swapping the class functions around at this point in the game is not very viable, what with development being as slow as it is. With that in mind, probably going to look at these with the current sin-type in mind.
Shadow Claw
Feedback: Although 5% crit. chance is now better than a 15% ATK boost, it's contrary to Hide.
Suggestion: Replaced with Battle Tactics.
Comment:I guess that's another sneaky hit. Yes, the Warriors and Knights could get the crit. chance increase instead, but the assasin should get the crit. damage boost. I wouldn't make it so overpowered as BT is right now, but it feels more natural for a DPS class to deal abnormal critical hits. And here, it's limited to a single class, not two.
YES PLEASE. xD
But seriously, even if this were to ever be implemented, it really has to be considerably lower than the current BT since we also have the random MoS proc - that would be a massive multiplier on our finisher - we don't need a sin Rage-Strike dealing 90k+ (in PVP; would probably be higher in PVE). Still, as melee DPS, we could stand to have some DPS increase - granted, there's no dungeon that really poses a serious threat to melee as they used to pre-AOV, but as close-ranged, a bit of increase in exchange for er, melee vulnerability would be nice.
Grimtooth
Suggestion: Remove combo point generation and healing effect. The latter would make even more sense on Cross Impact or Shadow Fiend than on grimtooth.
Comment:I'm sure you don't like that one, but even a 10% HP recovery would still be too much (still better than a Warrior's Tension Relax, a Knight's Aura Heal or a BMs Survival). The assassin should avoid being hit by using stealth and should concentrate on short & deadly attacks rather than enduring battles that causes a loss of life in the first place. Since he still has one of the best protection skills out there (Shadow Armor) and he is still able to use pots & soups, there is no real need for healing skills.
Mmmm, with the current sin class skill-type, I wouldn't remove the heal effect. Reduce it? Possibly. But not remove it entirely, not unless we see a boost in attack output or a change in dodge. We don't get bonuses in dodge, and in 1v1, I don't think the heal is significantly high enough to out-heal the DPS we receive. Probably the biggest issue lies in the full-heal-in-crowds, which the upcoming balance addresses (I think 10% across board, regardless of targets?) If we had bonuses in dodge, then yes, having a healing factor on top of that would be too much. But as the melee that seems to be meant to 'withstand' hits, SA with this (in reasonable amounts) doesn't seem all that unreasonable to me. Porting the heal to another skill (CI, for example) would have been interesting though.
And why would you take out the combo point generation? 
Shadow Armor
Feedback: I didn't like the old visual, nor the new one. To me the Rogue is more about running away, whereas the Assassin is about hiding & dodging.
Suggestion: No speed boost, no ATK boost, but a 20% bonus to dodge rate.Maybe a 5% increase in crit. chance as well.
Comment:If done properly, this dodge bonus equals a 20% increased in HPs combined with a 20% chance to avoid any harmful effects, like stun, freeze or one-shorts. To me, that would suit an assasin much more.
Somewhat random: the triggering of this skill has a slight delay which I do not like, but that might be my laptop, and not the game.
All these things combined surely changes the assassin from a mobile runner with regular crits into a more defense-oriented class that hit's harder on a critical hit. I think such a concept change won't find any supporters though.
A lot of your suggestions that seem controversial would be viable....IF, and only if, all your balances were taken into account (higher dodge, resettable hide. etc. etc the whole shebang). That is, unfortunately, as likely to happen as someone getting both a Blueseed and Redseed 50 back to back through runing. Any one of your suggestions, if modified without the others, would either make us too OP (resettable hide + SS? DAMN. Plus, stun-hide + SA +GT, wow), or weaken (SA 20% dodge increase isn't that large a boost if dodge is not outstanding in the first place) the current sin gameplay.
Also, I noticed your balances involves a lot of increase to our dodge and stealth, which, imo, have been given to rogues as their class skill-type. Sins, again, seem to have been restructured as the 'grin-and-bear-it' route, hence the more defensive skills. While it would be really cool to have a high-dodge sin again, the skill-stats reshuffle at this point in the game might be a wee bit too drastic. Again though, this is only my opinion - other veteran, more skilled sins might disagree with me as well.