I am happy that you have decided to play it safe.
Re. the water. Again, better safe than sorry. The big, American owned hotels have sanitized water, but local can be a different story. I have eaten in Cozumel, but keep in mind that only some places cater to tourists. It is possible to get sick from bad water or lack of adequate refridgeration...or ice. People can and do forget that the ice is made from water.
A friend of mine who is a chef for one of the cruise lines says that fish are the safest thing to eat, since it will smell bad if it has gone bad. Next safest are beef and pork, if cooked very well done. Riskiest is chicken or any kind of fowl. It can give you food poisoning while smelling and tasting fine.
I eat a large breakfast on the ship, then wait until I get back on board for a late lunch. I have heard, but don't know first hand, that the food at Chankanaab is safe. But, the big issue for food is the cost of keeping it cold before it is prepared. I don't want to be sick for the rest of the cruise! So, I take bottled water or, better yet, splurge some calories on a Mexican Coke....with no ice, just out of the bottle. They use an old recipe and it is SOOOO good. And I never drink soda at home.
Be safe, stay well and have a wonderful cruise!