Instead of the "Steady hand" class feature, I'd just give them the Weapon Finesse feat. If you absolutely must give them the ability to use DEX to hit on nonlight weapons, give them a class feature that reads like this:
Steady Hand (ex): The cutter may apply the the Weapon Finesse feat to non-light weapons.
Or create a new feat ("Improved Weapon Finesse") that allows this ability. The reason I suggest these options is that they are more "plug-and-play" with the existing system. Also, if you run a campaign, other classes that love Weapon Finesse - like the Rogue - can also benefit. As for DEX to damage, I think you could probably just add it on top of STR, rather than making it an either-or proposition.
I should also mention that the Disciple of Dispater (BoVD) does sort of the same thing as this class, with regards to making the character into a crit monster. There's also a spell (Golem Strike?) that allows precision damage and crits (I think?) against Constructs, at the very least.
By "Boring Class", I think Dominicius means that it's a full BAB melee class with a few buffs, but not very many combat options. It doesn't have any bonus feats, so it won't be able to Bull rush or Trip or Disarm like a fighter could; it doesn't have Spellcasting like a Paladin, Ranger, Psychic Warrior, or Duskblade; it doesn't have maneuvers and stances like the ToB classes, nor Rage like a Barbarian.
None of the classes I just mentioned are considered top-tier, but what they do have are mechanics that can liven up the monotonous routine of "I move and attack" or "I five-foot step and full attack"; they can self-buff with Rage or Spells and Powers, or they can use combat options like tripping and disarming. With the right feats and skill tricks they can run up walls, dive onto enemies, feint as a move action...
In short, they have options - plural. The cutter has one option.
I do like the idea of a class that fights with panache, creating a whirlwind of slashing fury. However, if you look at the Swashbuckler, Invisible Blade, and Dervish (I think they're all in Complete Warrior?), in addition to the Disciple of Dispater I already mentioned, you'll see that many of these character elements already exist in reasonably-playable form.