Just returned from caribbean cruise on Freedom of Seas, there were wheelchairs on our ship. Didn't see any restrictions as everything is accessible by lift. On any of the stop offs, we had, wouldn't be restricted as no steps. Did notice on their island in Labadee, Haiti, wheelchairs suitable for sand, first time I ever saw these. Do cater for everybody. Hope this helps.
It certainly is. Ships of the Royal Caribbean Line, NCL, P&O, Princess and Cunard sailing out of Southampton always have a number of buggies and wheelchair users among their clientele. Embarkation/disembarkation assistance is provided and some excursions are suitable for wheelchair users. Independence of the Seas is particularly suited to buggies and the bigger the ship the better really. Fred Olsen ships cruising out of Liverpool (ie Black Prince) are not very suitable due to narrow passageways and lifts. Talk to a cruise specialist at your travel agents and your detailed needs can all be sorted out.
Good advice may i add that as Mr Warman has some mobility that they could go on a few of the shore excursions as you need to be able to climb a couple of steps to access the coach and they can put buggy or wheel chair in the luggage bays.The newer the ship the better the access to all parts, from family experience RCI from Southampton they are big ships with plenty going on and reserved areas for disabled passengers ?go for and enjoy.
If you google 'cruise message boards' and click on the first link- halfway down you will find a section dedicated to accessible travel.