I'm with you on the common sense thing here.
But also in terms of rules, you still use the same skill "Unarmed Combat", so I don't think there is much room for interpretation.
I have much more trouble with TWS and a pair of gloves as technically or under the same statement you would still be unarmed. In terms of realism your movements don't change so the question why you shouldn't be able to use TWS without gloves comes to mind.
To be consistent I would either count hardliner gloves as weapons with which you then can use TWS (and make weapon focus out of them) but not Critical Strike or allow Critical Strike but not TWS (and probably do not allow the weapon focus thing either).
Personally I don't like the thought behind TWS as doesn't fit with my experience of how close combat works (I do escrima since 2001). When able to, you always use both hands, be it unarmed, with a weapon, or with two weapons. Even fencers (not the sporty guys, that's no combat) make good use of their offhand to grab, punch etc. But then again I have a problem with "full defense" but attack with your other hand!!! too, or to be more precise with its rules. Full defense as it is implemented implies "cover everything important, don't go down in a flurry of blows and pray he might just get exhausted". That leaves no room for a counter attack with your "other hand" (the one that didn't move in order to "suddenly" attack).
To cut a long story short, we changed TWS to a +1 dice modifier in close combat and specified it as the ability to use both hands armed or unarmed independently from one another (which is pretty difficult and more dangerous than just using 2 weapons). When going full defense or in any other situation in which your weapon (or unarmed combat) skill is doubled (like full defense) this modifier is also doubled. The bonus is probably too low to be realistic, but we left it as that.
[Edit]: Oh, and I have a couple of question for you. What do you want to do with him? What's his purpose/job in the shadows? He can kill most people with his pinky, that's for sure, but apart from that, what does he do? Many things kill, some with much less risk than unarmed combat, so in my opinion he needs something special to qualify as an alternative to a bunch of gangers, a car bomb or a sniper.