Shop the recommended stores, that way you get a guarantee from the cruise line.
There's a bit of a myth here. Recommended stores are not "recommended" because of their honestly and integrity. They are "recommended" because they pay the cruise lines a fee to get on this list. Plain and simple!!!
You really should have at least a ball park figure of what you're looking for, grade etc, and what it might cost at home!!!
The Caribbean truly isn't the shopping mecca it once was. What I think you will find is a great selection... which possibly makes it attractive to many.
St. Thomas gets far more cruise passengers visiting than some of the other islands, and therefore they don't seem as willing to bicker, and offer pricing as low as they used to.
If you're determined to shop, I'd recommend St Marteen more than St. Thomas. Less ships visiting, more incentive to make the sale. Don't be shy about making low ball offers!!