You dont need to show proof of age, but when I tried to book the Tulum ruins they didint let me because my daughter doest have 5 years. We are doing the Disney Wonder May 22 and she will be 5 June 2nd. (thats pretty close). It seems that the computer knows her age and didnt let the lady I talked to, book the excursion. She told me that I might get the reservation on board.
Hope you can do the Dolphin Encounter, we did it in Nassau last year and it was amazing and you dont really have to swim with the dolphins. That was my experience in Nassaul but the Passporter reports that in Cozumel the water is "chest high" or even "chin high" and that it could be over the heads for guests under 7, and that some cruisers felt the excursion isn't really great for cruisers 'under12' due to the depth of the water. My kids were 5 and almost 4 last year, but as I said before the water there was not so high.