Those are the same excursions my husband and our two girls took last year on our cruise. At Dunn River Falls they have lockers inside the grounds that you can use and the advice about cameras and foot wear is sound. This is a great trip and so much fun, our kids wanted to go down and climb back up again right away. The only down part is the hawkers as you exit the falls, they can be pretty persistent, I just look straight ahead and walk fast.
Swimming with the String Rays was the second highlight of that cruise, we left our belongings on the boat with no problem. One bit of advice, we booked the morning trip and were the first boat to the area and had the rays to ourselves for 20 minutes before the other boats got there, we were happy we opted for that.
The snorkeling in Cozumel is great, we again left our belongings on the shore with the tour operators, they put it all together and covered it with a tarp to keep it dry. We were not too concerned but we had only a small amount of cash, our room key and IDs and towels. Next time though we would bring our water shoes for the snorkeling because the beach is very rocky. They would not get much business if they were known for ripping off the cruise passengers.
Have a great time we enjoyed all these tours.