I'm actually plan a two week trip family vacation (me and wife) in this time frame - Nov 7 - 19
Cayman Islands is a potential in my short list of places to visit.
How's the typical weather during this time? Ok to swim in ocean?
We get the odd cold front swinging by which drops the temps to around 75 or so and roughs up the waters on 7 mile beach but all you have to do is go to the other side of the island and all is calm over there for swimming.
As for sharks, we are pretty much surrounded by a barrier reef and with shallow water inside the reefs there isn't much food for sharks so they don't hang out there. Even with as many scuba divers that come to dive the walls outside the reef I don't think I've ever heard of a shark attack here.
