I've not been reading this series since I dropped it pretty early on when i saw the "superior" gimmick (because that's what it is, a "how long can stretch this out before a return to status quo" gimmic) being repeated. but without his healing factor:
1) surely wolverines skeleton would kill him
2) even if it does, every time he pops the claws he would hurt himself
that said I don't see how removing his healing factor makes any difference. Every Marvel heal has an unspoken healing factor that allows them survive injuries that would kill a normal person.