We don't shop much, just sightsee. We have tours booked for some islands and then use an app called GPSMyCity which has self-guided tours for many destinations, including most of the ports we are visiting. Costs me all of US$13 per year or something like that and you can download to use online. Renews via Google Pay. And sometimes we just hit a beach.
We have five sea days and 8 ports, of which 5 are ones we have been to before. I can't even remember them all right now. The ones that aren't repeats are Antigua, Dominica, and Grenada. This type of cruise is really not my first choice. They're getting a bit old hat as you suggest. But my wife finds resorts boring compared to island hopping on a ship so this is how we spend our winter getaways.
Personally, I would happily hit a good resort in the Dominican or something, pack my laptop along, and write on the balcony or something. I have staff from St. Lucia and the Dominican Republic on my team so can even get hot local tips if we go to one of them.