I think you should take your real rings. You shouldn't worry too much as long as they fit right. I wore my e-ring (and wedding band after the wedding) the whole time I was in Mexico and they never came off. I went swimming, snorkeling, rappelling, ziplining, and swimming with the dolphins and they didn't budge.
Also if your room has a safe you can leave them in there or have some less-active family members hold on to your ring while you are in the ocean