Since getting my J Pouch I have been in numerous Caribbean and Latin American countries and never had any problem- this included a trip all over the Yucatan Peninsula in Mexico. However, I wouldn't worry about just the water but also the food. A friend of mine went to Costa Rica and ended up getting campylobacter food poisoning from undercooked chicken he ate at a Costa Rican restaurant. The result was he spent the majority of a planned 7 day land vacation in the hospital.
If you are on a Cruise, the majority of your meals and beverages will be on board. As previously noted they have bottled water and are familiar with the gastrointestinal dangers of travels to foreign countries.
The only weird thing that ever happened to me was in Jamaica. When I was in Jamaica, there was a very bad outbreak of Dengue Fever, a mosquito borne illness. The US Center For Disease Control had issued a travel warning for Jamaica the week before my trip, which at that point was booked a month in advance. When I got to my resort (in Negril) I asked the resort concierge about the issue. He then told me the resort sprayed the area around the resort with pesticides and that the Dengue outbreak was mostly in mountainous forest in interior areas of the country. Negril is on the coast.
During that trip, I noticed barely any mosquitoes and had a great time. However, on the next to last day of my trip, I woke up and my ankle had swelled up like a grapefruit. Even since then I have not seen a sprained ankle that was more swollen. I didn't feel any pain but the appearance of the swelling concerned me greatly. I was certain I had contracted Dengue Fever. I actually wrote a letter to my parents which essentially told them I loved them and would miss them, in the event of my death.
All that they had for medical treatment at the resort was a nurse's station with a red cross on it. I waited until it opened for the day and it was staffed by an American nurse. She took one look at my ankle and she said to me, "honey you have a spider bite. I have a salve that will help that." I then applied whatever salve she gave me and the swelling went down by the end of the day. When the plane safely landed in the USA I tore up the letter I wrote to my parents.
I did see assorted spiders during the trip, and I assume I was bit while sleeping in the hotel room. It must have been one of those tarantulas, like the one that crawls over James Bond in the movie "Dr No" (which was filmed in Jamaica). Of course if you are on a boat this should not be an issue unless they have stowaway spiders.