I love cozumel, I would hate to see you miss out on it. go to chanacanob. it is a beautiful beach, it has a few mine ruins, a swimming area , a beautiful lagoon, a place to snorkel ( buy your snorkel gear on the ship for a few dollars) if you want to spend a few more dollars you can swim with the dolphins. It use to be super busy but hurricane Wilma (I think thats the one) tore it up pretty good. they rebuilt but the crowds have not returned. I absolutely love it.
also I feel like it is a safe island. Enjoy it,