I'm sorry but this is wrong. You are disabled!
Just as everybody who wears glasses for vision correction is disabled. You just don't think of it that way. Those of us who are regulars on this board try to not think of ourselves as disabled but just having special needs to be as everyone else.
But the normal (and official) suggestion from Guest Services for a mobility or stamina situation is the suggestion to rent a wheelchair or ECV. If you go to Post #2 of the disABILITIES FAQ you will see lots of information about wheelchairs and ECVs, including Disney's fees and recommended off-site locations.
I hate to disagree Cheshire, but some of us regulars on the board are fine with thinking of ourselves as disabled. I am not differently abled (i have no special skill related to my health) and while i have special needs, that is not how I think of myself. I think it is fine to think of oneself as disabled. It is all about the terminology one is comfortable with. For instance, i am fine with disabled, but hate the terms special needs and differently abled, when applied to me. Others can use whatever terms they are comfortable with.
And I am not ever "as everyone else," but that has little to do with my disability!
Anyway, to the OP - I would definitely bring the number of an ECV company, just in case!