Back to your question on if there are photo ops in the port areas... I actually did this itinerary back in 2014 (so it's been five years - wow, felt like yesterday!) and can share my photos for an example of what there is to photograph. At the least, it will give you an idea of where the ship docks and how accessible ship photos are from the immediate port area.
Falmouth, Jamaica -
http://www.victoriaonvacation.com/2014/06/2014-disney-fantasy-western-caribbean-Day5.html
If you want photos of the Margaritaville area, it's immediately where you dock, so you could take your camera off the ship, then take it back to your room if you're leaving the port area. I was definitely struggling with lens fog in Falmouth.
Cozumel -
http://www.victoriaonvacation.com/2014/05/2014-disney-fantasy-western-caribbean_27.html
There are actually two possible docking locations in Cozumel. I believe the Disney ships dock at the "old terminal" Punta Langosta - but once we arrived on another cruise line and docked at the "new" (it's been like 10 years now since it opened) terminal Puerta Maya.... I think mainly Carnival/Princess ships dock over there.
So you're staying on the ship in Grand Cayman? Not a bad choice. I've been to Grand Cayman many times, and the last time we were there, we realized we would have rather stayed on the ship that day rather than dealing with tender lines.
I have a D7100, not the cheapest of the crop sensors, but I'm not sure I would be as adventurous with a full frame camera, so I understand your hesitation is greater than mine! If you're really serious about getting those better-than-phone photos, you might consider buying/renting a "cheap" D3500 kit. Maybe that's crazy?? But, I mean, a D3500 costs less than a quality full-frame lens, so if you consider that, maybe it's a reasonable option. I'm just throwing this out there because I think if I were ever to upgrade to full frame, I would still want to keep the D7100 for adventures.... but maybe not. Maybe once you go full frame, you never go back?!
Tom Bricker travels with his full frame camera and has been into cruising lately. He's a photographer for a living, so I just assume his camera is always on him. If his photos don't make you want to bring your camera, then you should definitely leave it on the ship!
https://www.disneytouristblog.com/3-night-bahamian-disney-cruise-line-report-part-3/