[milesdyson]

If it gets heads up with CO on the turn, I would check call the turn and either check call the river or bet/fold it (likely just check call after the turn K).

If it goes to that turn 3-way, I would check call again and reevaluate on the river. If it were a low turn card, I would likely check call 3-way once again, and then lead out on the river.

Having the flop check through is so far from a disaster, and it doesn't happen too often with a CO vs. the blinds hand. CO will bet the flop with ATC more than often to make up for any value you miss from them calling with worse hands on a AKx board.