2nd in chips, folded to me on Button (AKo)

[Shakespeare]

This is $55, 4 left, I am 2nd in chips and cover the biggest blind by 800 and have AKo on the Button, its folded to me.

I decide to push. After thinking a while, the SB (tight) makes a loose call with A2o and catches his two on the river, Such is life. This got me thinking on how I could have played this differently, not because I think it’s a bad play (?) but because of what I had been doing previous to this hand.

I had push a few other hands with 4 left, it was folded each time. When the AK came up, maybe I should have made a different play instead of pushing? maybe raise 1/2 of their stacks, and put them all in on the flop (no matter what). The only problem I can see with the 1/2 stack bet, is if they use the stop and go play.

So basically my question is, should I still have pushed, or is there a better way to play this?

Sorry, I think the blinds were about 150/300, maybe more.