Push the flop.

Barring that, check-raise the turn all-in. I say this because if you push the turn, he's probably folding any hand he has without a spade. If you check, you induce him to bluff (although I'm almost positive you're beat), and then he's committed to call your c/r with or without a better hand. Plus you have the outs to boat. If he checks the turn behind, then you can check/call a reasonable bet on the river.

Check/calling the turn is SO WEAK here. But seriously, just push the flop.