Why would White play g4 at once? The Knight on h5 isn't threatening anything - well, Nf4, but that can be ruled out by g3. What would you do after Nh5, Qc2 g6, g3? If f5, then white simply castles (again, black isn't threatening anything), after which he's ready to hit back with g4 / f4.
I assumed that's what you were suggesting - Nh5, Qc2 g6, g3 f5, O-O Ng7, then look at his position - only useless moves and we're threatening multiple attacks.
What attacks? We wouldn't be threatening to play e4, nor would we be threatening to play f4 (f4, gxf4 exf4, Bd4 just places his Bishop on an excellent diagonal). White is able to play on the kingside as well, with moves like Kh1, Rg1, etc.
Nc5 looks like a far better move. Nh5 is far too slow and stoppable, with no force whatsoever. Nc5 forces a hand-revealing move, and it seems like we'll fall even at worst, and most likely we'll have an improved position by moving either the knight or the bishop. switch votes to Nc5 if you could.