I think the issue they are worried about with the cruise ship is that it probably won't fit through the cabin door unless you are in a HC cabin, which I assume you are not. My
scooter is the same width as a wc and it could go through the cabin door with a lot of maneuvering, some bumping of the wall, door frame and door, and there was no room to spare. I don't think that you could get the larger scooters in there. So then the question would be if there is somewhere else it could be parked and charged. I did leave it outside the door several times if we were just there to change clothes or something and weren't going to take long. But the halls are narrow so it would be in the way if it were there for long.
I would ask on the
Disney Cruise Board and see if anyone there has ideas or has dealt with this before. If you are on another cruise line check out cruisecritic.com.
I know you mentioned not having a place to store it if you rent for the week and don't take it on the cruise, but if you are staying on site you may be able to ask Luggage Services to hold it for you while you are on the cruise. Also you could just arrange for Walker to bring it for the day you will be in the parks, pick it up the next day and then another rental with drop off/pick up when you get back.