Hi Nicole,
Welcome to the Moms Panel! As a mom of a five year old little boy, I've spent a lot of time researching the port adventures for our upcoming Eastern Caribbean cruise.
While in St. Thomas, I these are the adventures that I would consider:
Magens Bay Beach Break - This is probably the most family-friendly beach (other than Disney's own Castaway Cay of course). With it's calm waters and family-friendly beach, this excursion would be perfect for a solo parent and a small child.
If a day at the beach isn't quite what you are looking for, you could try
Coral World Ocean Park . It's not something that will take up your entire day (the park is fairly small) so once you return to the dock you could walk over to the
butterfly farm. I like the idea of having something "to do" that is only a three minute walk from the ship. So if it's not up your son's alley, you can head back to the ship as soon as he is ready.
As for St. Maarten, I am thinking that the
Golden Eagle Catamaran adventure would be a great memory maker. A catamaran ride is always so exciting for the kids, and although there is plenty of time to snorkel, you could opt out and head right over to the beach if you aren't quite comfortable snorkeling. When I did it with my little one, we would link arms and as soon as they relaxed and realized how easy it is - it was a lot of fun for both of us.
You can read about all of these port adventures
HERE.
Hope this helps, have a great time!