Yes it depends on which cruise you go on my wife is confined to a wheelchair and we have been on the P & O Arcadia and Oceana with no problem.
NO problem. royal caribbean are good for most disabled people.Good luck.
One caveat. This may not apply, but it depends if there are any 'tender' ports. I have seen people with walking sticks, agile enough around the ship, to be refused entry onto a tender if the water is choppy.