Just to let you know what I experienced ...
I am an able-bodied person who just booked a disabled cabin on the Monarch (and yes, 'cause it was bigger).
The agent asked me directly whether I was handicapped, and I answered "no." She just said to be prepared that if a disabled person requested a handicapped cabin, I could be knocked out, which I said I had no problem with in that my Mom is in a wheelchair part-time.
I booked the cruise 3 weeks outside of sailing, so I don't think I will have any problem, but I thought I would let you all know how it was handled in my case.