I have been on both Braemar and Boudicca (Fred Olsen) and they are nice sized ships - they also do some of their cruises out of Leith. I have a wheelchair for shore tours and have had no problems getting about the ships with the chair. I have just come back off the Boudicca and there were several people who were in their chairs for the whole trip. Boudicca does have some wheelchair access toilets on the public decks, I know Braemar doesn't. Both ships have cabins adapted to take wheelchair users. I am not sure how they get wheelchair bound passengers onto the tenders - I was able to walk down the steps and they carried my chair on. When we were quayside I walked off the gangway and my chair was carried off for me. Boudicca also reserve tables in the Neptune lounge (where the shows take place) for wheelchair users. I have always found the staff on both ships extremely helpful and kind.
I think most cruise ships are suitable for wheelchairs and cater very well. If you prefer a smaller ship try Fred Olsen. We cruised with them last November and there were quite a few people in wheelchairs and some using electric 'buggies'. The staff were great and very accommodatin.