Pushing after the flop is very reasonable. we have 15 outs to win if he has an overpair and much more if he has ak or aq.
The only problem I have with pushing after the flop is my position in the tourney.
Hero is in a very good situation now. If we push all-in and vilian has any kind of hand ( 1010 - QQ ) he will call, and that will put us in a coin flip situation. (after the flop AKh is 52% favorite to win QQ for example with this flop).
I'm not sure I want to risk my all tourney for a coin toss at this point. ( if I had a shorter stack it might justify it).

as for raising preflop with AKs. Vilian is a very tight player if we raise and he reraise what then? maybe calling and seeing a flop with a better position is better. (If I was on BB or SB maybe reraisng is better to eliminate the position advantage)

what do you think?