I had called Disney regarding excursions in Nassau when I was going to bring my 15 year old godson who was in a wheelchair and their reply was that since it is not the USA nothing is really set up for handicap accessibility there, the buses don't have chair lifts etc....you could wheel the person down the road a bit to the straw market though the aisles there are a bit narrow for a chair but it may work (I am trying to thing back as to how narrow but perhaps someone that just returned could give you an idea on that) Or just wheel them around town to the shops. Best thing might be staying on the ship and enjoying the ship since you are only on a short cruise, I know others have different opinions but as far as I am concerned you won't be missing anything by staying on the ship.
