I've skipped Freeport a few times is all. You should at least take the short walk on GC to Abanks and get some conch fritters. I might could miss a few ports on the Dream to explore the ship, the Elation probably not as I know those ships very well.
Besides if you don't go ashore you can't really say you've been there. I remember being ill the first time I went to Dominica. I was still determined to walk to the end of the pier and set foot on the ground. Cozumel is one of my favorite ports. You can read a book under an umbrella at Paradise Beach. Rumor has it that Tom has wifi set up at the bar now so you can check your email etc. if you like. I just can't imagine staying on the ship unless I had to. Then again, I am more acclimated to hot and sticky weather than you are probably, and even I don't cruise in July.
To borrow a phrase from the Nation of Why Not.."Get Out There!"