Jaguar Paw does not have thatch cabanas -- the 16 rooms are in four units.
As to swimming at Chan Chich, there is a beautiful swimming pool which opened a couple of years ago -- nicely done with a netted top to keep out bugs, lots of tile, a small artificial waterfall. There is also a lake near Gallon Jug.
Regarding caving around Chan Chich, I'm not sure. Most of the better-known large cave systems in Belize are farther south in Cayo and Toledo districts but there are some in that part of Belize as well, especially south of Gallon Jug. Don't know what you could visit, though. If caving is a priority, then I would think you would want to spend most of your time in the Belmopan/Cayo/Chiquibul area, and of course Ian Anderson is known for his caving trips.
Belize First Guide to Mainland Belize http://www.turq.com/belizefirst/