I'm absolutely c-betting here, to get a free card later if for no other reason.
If Button has an ace of any kind he's not folding. But if he called with a middling pair that ace is the last card he wanted to see, and you must give him the chance to fold his 66 or whatever. Besides, the Ten is coming!
The more often that we can get a free card on the turn, if we choose, the more inclined I would be to bet this flop. We also have a non-zero chance that they will all fold the flop.
I bet here. Anyone folding small PP would be nice and I getting the button to fold would be great for the turn action. The real question is if you only get one call from the blinds do you v-bet the turn UI?