I did that once and it was so worth the money. It's not a ship excursion though. Here's what I did:
There are 2 Sandals resorts in Ocho. One is closer to the port and very close to Dunn's River Falls. We went to the Falls with the excursion group, then grabbed a taxi and went over to Sandals for the rest of the day. It wasn't cheap.. I think it was either $100 or $125 for a day pass (but I could be wrong it was a few years ago). At any rate, it was well worth it. A beautiful resort with lots to do and great drinks! Also, this was the first time I had ventured off from an official ship excursion.(I'm sort of a chicken). Anyway, it turned out just fine.
I would call Sandals before you leave to make sure they still offer day passes.