It's uncommon (though definitely not unheard of as we do get wounded warriors on our local boats from time to time) to find canes, wheel chairs, etc. on dive boats. Also, inanimate objects don't usually have a way of getting under foot on a pitching boat. Space is at a premium on a dive boat, unless you were going to charter the whole boat and bring your dog on board (I can't really see any reason why someone would object to this approach) it's unlikely that there would be room for the pup. I would personally worry about tanks rolling around, people falling over on or in some other way harming the dog. As a passenger I'm sort of routinely covered in mystery bruises from being run into with tanks. I'd hate to put my pup through that.
One local boat that I crew on occasionally does have a boat dog that belongs to the Captain. The dog is kept in the bridge and cannot get to the dive deck. It's not without its challenges as not everyone likes listening to a dog bark on their dive charter. I think you'd be best finding an operation that is willing to work with you and/or looking into a boat ownership situation or co-op where you can make the rules. I don't think it's impossible, but the standard weekend cattle boat seems like it would be a challenge for your particular needs.
