You don't have to kill it to tell, but unless your boat has really low sides (not the best for the ocean) you have to bring 'em aboard to tell. Once you do that you are legally obligated to tag the fish. Technically, at that point the fish is legally dead.

That aside, here's how you tell. Lift the gill plate and look at the translucent apex of the collar where it inserts mid-throat. If you see red there, it's a red king.

Look at the pic below. The upside down kings are obviously red by looking at the cut open belly cavity. But now look at the other two. Even though you can't see the red meat in the belly cavity the red patch at the tip of the collar is the dead giveaway.... and yes, without having to kill the fish.