Welcome to cruise-chat. First of all, there is no need to take you passport off the ship
. When I went cave tubing I left my wallet locked it the van that drove us to the area. Never heard of anyone having any problems. Some people carry those plastic waterproof containers you can put around your neck. It holds money and your I.D. cards. If you don't have one, they sell them on the ship. Cave tubing is the greatest thing you can do in Belize.