Unfortunately the island isn't the best for the handicapped. The terrain is mountainous and wheelchair access is limited. Magens Bay has access to the water via a ramp (a relatively new addition) and some restaurants are handicapped-accessible but I'm having a hard time coming up with any resort that can really boast being handicapped accessible.

It is a volcanic island and there are quite a few hills, some of them rather steep. I believe the building at American Yacht Harbor in Red Hook has an elevator. That would get you to Caribbean Saloon, Island Time Pub, Molly Malone's and several shops. Big Bambooz is right next door and is street level. XO Bistro and Duffy's Love Shack are right across the street --- and up a hill on either end of the lot although the west end is easier (not as steep) than the east. Havensight and Yacht Haven Grande are both street level and have plenty of shops and restaurants / bars. Here is a web cam I like - the cruise ship dock in the foreground is Havensight and the docks to the right are YHG. Have a good trip.
http://paradisepointtramway.com/webcam/webcam.html

The hotels (The Reef, Sugar Bay) are probably accessible. Secret Harbour has one (maybe two) rooms, but these are not the condo units. I know I have seen sand chairs at a couple of beaches, but don't know if they were private or not.

i took my dad down to st john in 2006, he has one arm and one leg and gets around on crutches. we stayed at the westin and everyone there was excellent with getting us from one place to another. it was a little difficult for him when we were in the cruz bay area, we tended to get to one place and stay there. the cab drivers were awesome with helping him in and out of their vehicles.

i'm not sure how limited you are but it is possible, just limiting.

hope this helps!