In general the larger and newer the ship the more stable it is and in general easier to get around..
Getting on/off the ship:
For transportation from the airport to the pier, Hydraulic Lift Transfer is sometimes available for guests with mobility limitations if requested in advance.
Ports in general use stairs or gangplanks or airport-like jet bridges to move passengers. Depending on the tides these can become very steep and often the lower gangways can not be used.
The lower the tidal difference, the easier it will to get on/off board.
The map below will show you the low (blue) and high (red) around the world:
Areas with no or little tide differences are:
Baltic Sea including Oslo.
Areas with very high tide differences are:
North East Canada (Bay of Fundy 12 meter!)
Cook Inlet USA
Bristol Channel UK
At a tender port, the ship isn't able to pull up to the pier or dock, usually because it's too shallow. You'll be loaded onto a small vessel called a tender, and taken to shore that way. Sometimes if there are a lot of ships at a regular port, some of the ships may have to stay offshore and bring their passengers in by tender. In general, only collapsible wheelchairs and rollator walkers are accepted.
This list is a guide only, sometimes smaller ships are able to dock.
West European and North American cruise ports cities are in general "wheelchair" friendly.
For other health issues consult your agent or cruise line before you book.