You have a very good stack here. I don't think you need to risk it all pre-flop on this hand. You're first to act after the flop. I can see two other reasonable options:

Call the raise and push any flop wihtout an A or a K. Continuation bet any A or K flop and fold to an all in.

Alternatively, you can re-raise about 7500 to make Villian define hand.

I don't know if the nature of a satellite structure makes a push better or worse, but there is more than simply a push here to consider.