Not sure what kind of woodworkers you seek. One fellow on back street (just west from Chinatown) has a sign out that say "wood shop", not sure what sort of work he's doing. There are some local carvers in the palapa area of front street. Be sure to check out "Major" across from "Friends" Lebanese restaurant. He works only with machete, chisel and sandpaper (he carved full size dories as a younger man). Long known for it's shipwrights the days of traditional boat building on the caye has sadly passed. I'm sure there's plenty more woodworkers I'm forgetting about, just ask around. Be aware though that someone sanding wood behind a table of fine wood carvings did not necessarily make them himself.