push in this situation every time.
the reasons being:
1.your short stack,you may never get a better hand dealt than this.
2.you have AK ,the worse position you can be in is that he has AA, even against KK you have outs.if he has any of them hands then so be it.it was not meant to be.any other hand your almost 50/50.

3.if you push all in you will get to see all the 5 cards and you will also get to isolate the raiser and getting heads up with him if he calls which is in favor of a hand like AK .the reason is that in heads up situations top pair is usually enough to win the hand so getting to see the 5 cards is very important.

4.you have some fold equity so he may fold in which case you win the hand right there which is not a bad pot.

never ever fold AK in this situation,its a very powerful hand in this situation.
the only reason why you would think abt folding AK here is if you had a very very larg stack and the villian also had a very larg stack that he could bust you with.in this case you could argue that you have enough chips to buy you enough time to look for a better spot.
but here you dont have that many chips at all.
also the worse way you can play this which is even worse than folding is to just call.
if you just call,miss the flop,then you have no idea wheather he has AQ or KK if he pushes.you will have to fold or take a chance to see the other two cards.either way you ahve made a mistake and the villian has gained from your mistake.
hope this makes sense.