To add to what Kathy has said, decide quickly and book if you want to go to Little Cayman. Another recommendation for the Little Cayman Beach Resort from me. Great resort all around. But also consider this.
There is pretty much only one way to get to Little Cayman and that is taking a twin otter from GC to LC. Those planes typically hold 15 to 16 people so space is at a premium. If you decide on LC, YOU CAN'T BOOK THAT FLIGHT SOON ENOUGH. Lots of ways to get to GC but one way to get to LC so don't hesitate on that flight.
I think their last flight to LC is around 5:00ish in the afternoon. They also have one in the 3:00ish range as well. What we typically do is book one of the later flights to give us plenty of time to fly to GC, go thru customs, get our bags, and recheck them to LC on Cayman Air.
If you have some flexibility on travel days for your week, you may want to consider going Friday to Friday. Most folks fly Saturday to Saturday and the airport is packed and those seats going to LC sell out even quicker. Even Sunday to Sunday is likely better than Saturday to Saturday.