You are in luck....all three of those ports are safe and easy to do on your own!!
Every port seems to have the "thing to do"...
Belize is cave-tubing. Now it does require some walking, but it handles a wide age range.
We use this
(Yhony) It has been a couple of years, but he was $45.00 a person. (plus a small tip if they do a good job)
That was for 2 caves and you are LINKED TO A GUIDE (this is MOST important...I would not do a cave tubing excursion without this safety factor).
Oddly enough, in the past, ship excursions only link you to another person...that is NOT sufficient. If you are linked to a GUIDE, the guide directs your flow and keeps you away from cave walls that may have spiders and jagged rocks etc.
I have been reading about Yhony since 2004 and have never read where his tour has missed the ship. I would get the 9:15 excursion. You are tendered into Belize...so make sure you get an early tender.
Roatan - Mahongany Bay was not our dock the last time we were in Roatan but I understand it is a wonderful stop....so I would suggest that...IF no one wants to go zip lining with Victor. He runs a great independent tour.
Grand Cayman - Capt Marvin swimming with the stingrays is the independent tour to do. This is a VERY expensive port. There is also 7 Mile Beach which you can just grab a taxi to from the port.
Hope you have a wonderful cruise.
Edited to provide link.