Hi Crys,
When we were in Bermuda we docked in St. George, but in Hamilton the cruise ships dock directly across from a really pleasant shopping street. It would not be a long walk. Also, there are benches on the dock side of the street, so for a breather you could cross back to that side and sit and watch the people go by. The Hamilton downtown area is hilly, so beyond that first street facing the dock you would have a bit of a climb, as I recall. We spent only part of one day in Hamilton, and I'm not much of a shopper, but I bet others will be able to give you more guidance on the good shops, etc.
It happened that our time was such that we didn't take any of the ship's excursions, so I can't remember exactly what was offered. However, there are several ways to get around that are good for a non-walker. The ferry system would be a lovely way to see the island from the water, and believe it or not the public bus system worked well between Hamilton and St. George. Taxis are readily available, also. If we ever go back, I will be arranging a taxi tour to get to some areas of the island that we missed.
St. George, by the way, is a lovely little town, much smaller than Hamilton, and I highly recommend a visit there, as well as to Fort St. Catherine near St. George. Like Hamilton, St. George is built uphill from the water, but a little shopping street fronts onto the water, and the visitors center and a town square are right near the dock and the shopping area. We took a taxi to the fort from the St. George town square (probably a five-minute ride, if that).
All in all, I believe there are some good options for a non-walker. You will love the trip!