The only time I've been to Grand Cayman, I did a Stingray City trip organized through the ship, as that was my first time to Grand Cayman, and heard that was the "don't miss" type of attraction in Grand Cayman. Swimming with the dolphins sounds exciting as well.
However, in Jamaica, I would HIGHLY RECOMMEND sticking with a ship's excursion, since they scope out the tour operators, and have contracts with the more reputable ones. The only thing I didn't like about Dunn's River was all of the vendors, especially since you have to walk through the area where they are to exit. If you didn't want to do a ship's excursion, then maybe check out Shore Trips online at www.shoretrips.com
. They are another reputable company that looks into the local tour operators. I wouldn't just wait until you got to Jamaica to book an excursion.
One thing I would check though about Grand Cayman, although you've been there before, so you probably know the drill. Since that's a tender port, there's a chance if the weather is rough that it may be deemed too dangerous for the tenders to run. If you book with an outside company directly, and not through the ship, check what their policy is if you are not able to make it to port on your scheduled day, or if you have to skip the port all together. This actually happened to me on my last cruise. It was pouring rain, windy, and rough seas, and the port decided it was too dangerous for the tenders to run. I had an excursion booked through the ship, which they refunded by means of an onboard credit. I would think though, in the winter, there's less likely of a chance of that happening than when I went (early fall 2010).