$10 sng, KK in bb -- stragegy?

[Javanewt]

This is my first post in this forum, so sorry if I do something wrong.

Blinds are 50/100.

I have ~1600 chips in the bb with KK.

UTG raises to 350 (stack ~3500)

Folds around to me.

UTG has been fairly aggressive but won his chips legitimately. I know I must push. If I push, I think he will call with a decent pair or a big A.

However, is there any use in just calling and pushing the flop, regardless, since I plan to get it in anyway? Might UTG fold if he doesn't hit?

If he calls my push, he knows he gets to see five cards, but if I just call and then push the flop, he has to think about it for another 1250 chips. Can this work? Is it a good idea or is it wiser just to get it in with KK now?