first with using a
scooter. I think this will make everyone the happiest. He'll be more independent and no one will have to push a wheelchair if you can make it work for him. If you do an outside rental for a scooter he'll have the scooter everywhere he needs to go.
You can go to a grocery store or a local scooter store which will have one similar to what he will use at Disney. The local store will demonstrate one; so, you'll know how to take it apart and so forth. Try to see the Pride models. Many Pride scooters are rented in Florida. A local zoo scooter rental would be your best answer for a trial run of sorts. It would be all day and you could see how he does with one. Disney will be harder than a local zoo. I can see how turning and parking could be an issue. In those cases someone else may have to take over. We took an aunt and she did all the easy stuff with a scooter. When it came to the harder stuff I took over (getting it on and off the buses, for example). The grocery store model is not the same and it may be too hard; it's quite big and heavy and it has a basket making it very long. I'm not sure that would be a fair test. If he can do a grocery store one he should be able to handle a scooter.
I think speed will enter into this equation, as well. If he takes turns slowly he may be able to manage. You don't want the scooter to tip over and without control with both arms and hands this is trickier.
You can always park the scooter for a while and come back to it if he wants to walk some. Just make sure you take the key and park it somewhere out of the way of traffic.
Also, I would caution you about going in and out of some rides where you have to take a step up or down to do it. Someone should be on both sides of your father. One in front of him and one in back as you get on and off this kind of ride. I would be careful with rides that have walkways that move, too.
If the scooter doesn't work out getting a wheelchair is another option. I wheelchair my mom around the park for 10 days; I survive. I'm in my sixties pushing a manual, transport chair. Don't make him feel bad in any way if you need to go this route instead.
