Good call. We bought costume jewelry "replacements" for our honeymoon trip. My wife's diamond was my great grandfathers, so while it would be easy to replace it, I would never want to. My ring was the first time I've ever worn a ring, so I wasn't sure how I would do with it, so I wore a replacement as well. We did see one guy lose his ring when cliff jumping. I'm not worried about theft at all.
After several years and further visits to Jamaica I don't really bother with the replacement ring anymore as I now know that my ring is secure. But with a new ring, I'd not take the risk. The wife does wear her CZ ring during the day just to be safe, the good stuff comes out at night
We bring ours and leave them in the safe during the day because I don't want to worry about it coming off. It's hot there so my fingers swell a little but they also get wet and I just don't want to have to worry. We wear them after we shower before dinner since that's about the same as wearing them at home. One thing to remember it to BRING SOMETHING TO KEEP THEM IN WHILE IN THE SAFE!!! Seriously. The safes have a little space around the edge that is just the right size for jewelry to slip into and it is nearly impossible to get it out once it is in there. Bring a ziplock baggie or a little container or something.
we both wore r rings there. if ur body isnt used to the humidity ur fingers will swell up. my band is a lil loose and my wifes ring is just the right size. the first night there i literally almost pulled her finger off trying to take her ring off cause her finger was turning blue. i never took mine off even at the beach.