As a native of St. Thomas I can assure you that if there are ships in then shops are OPEN.
But do your shopping at Havensight, prices the same as in town, not the widest selection but very good just the same, buy liquor at Al Cohen, I fyou have lots of time and there are not more than 1 or 2 ships in, then go downtown, it's nice to see, otherwise shop at the dock and save time and crowded conditions. Use the time to see the island - it's beautiful, especially the Magen's Bay, Drake's Seat area. The east end (where you catch the boat to St. John) is not so nice, no need to venture that way, the far west end is not too populated so the near North side is the best for views, etc. Hope this helps and have a GREAT time!
I have been to St. Thomas numerous times and have shopped both downtown and the Havensight mall (both in one day).
For a wider selection head downtown, but beware there is soooo much to choose from your head will be spinning.
I found the Havensight mall to be more enjoyable and the prices even better.
Last year I bought a slide downtown and saw the same one at the Havensight mall. It was cheaper. I asked the owner why, and he said that downtown hires sales people and they work on commission where the mall is family-owned and no need for commission-based sale people.
Also, it will cost you about $6 per person to get a taxi service downtown. The Havensight mall is within walking distance and very enjoyable.