Sure - Grand Cayman and Cozumel both have nice jewelry/watch stores close by the pier.
Be prepared to declare your watch purchase with customs!
I wear a fairly expensive Rolex watch that I have had for 2 years, and upon my return I was stopped and asked by the US Customs inspector "How long have you owned your watch?" She asked me to turn my wrist so she could inspect the band clasp. I guess she saw enough wear to assure her that it was not purchased on the cruise.