Howdy there...
Congratulations on choosing a great vacation option! I have to warn you though...cruising is addictive! You won't be able to stop at just one!

I don't think you're going to have much trouble on the ship or in port. On the ship, there are usually elevators everywhere. The decks are easy to walk around on. The cruise lines have thought of these things. As a matter of fact, you'll be amazed by the amount of folks you may run into in wheelchairs or who are elderly! And truly, what would be a better way for a person with limited mobility to see the world? So if they can make it okay, then I surely think you will.
As for excursions in ports, snorkeling that you mention in particular, most of the snorkeling tours will require you to wear an inflatable snorkeling vest, so if you can swim reasonably well, you should have no trouble. But, bear in mind, only you can make the final decision as to whether you feel safe in any situation. I see you're going to Cozumel, and I'd certainly like to recommend the Chankanaab Park excursion! Chankanaab Park has snorkeling, places to shop, dining on the beach, dolphin excursions and more, and is one of the most beautiful parts of Cozumel (and I've seen Cozumel from top to bottom, and all the way around). If you look on our home page, there is a Featured Port Review on Cozumel, and it has pictures from Chankanaab.
Hope this helps...have a great vacation!
Smooth Sailing,
--Johnnie