I think if he's alone with a
scooter this would make me anxious. It sounds like this could be the case with him at the resort alone. Scooters are mechanical and they can have failures. Batteries can be up and down on charge depending on how old they are. What I mean is that some hold a charge (if newer) better than others. What if he gets stuck somehow? I believe Disney would help move the scooter or whatever in a bad situation, but it could be difficult for him to get a Disney cast member depending where he may be. If the scooter is only being used at the resort I would think your battery charge should last, but there can be other issues especially if you are outside (like if he wants to sun bathe by the pool) with a scooter and it rains. We had one bad experience with a battery ourselves. In fairness, we have probably rented a scooter 50 times or so. The odds are in your favor for nothing to happen, but I always feel like I will be the lucky one to have something go wrong.
Also, I think I would insist on a ground floor room. You don't want your father dealing with elevators being on a scooter by himself, not as a double amputee. If he doesn't have a rollator walker and he uses a regular walker I would absolutely get a holder for the walker to be on the scooter. It fits somehow on the back of the chair on the outside of the scooter. You can rent walkers, too. This will make the back end of the scooter a little more bulky.
Another point is balance on the scooter. Most people believe 4 wheel scooters have better balance. Most people believe 3 wheel scooters have better manueverability with turning radius. You may want to consider a stronger and heavier scooter for stability and battery charge. The smaller, portable travel scooters in my opinion have a little less stability; although, this is what we use all time. The rental prices vary and get higher priced for scooters the bigger and stronger they are.
I would strongly recommend if he's going to be alone on a scooter and ventures out of his resort room that he have a cell phone on him and be ready to use it in an emergency. Have his walker with the scooter, too.
If he has never done a scooter I would find a way to practice with him. Go to a mobile store and try both a four wheel and a three wheel scooter and see which one he likes better. Try a portable, travel scooter and a bigger one, too to see if this makes a difference for him. Usually, you can go for a test drive in their parking lot. I alway like to use a zoo to practice with a scooter when you are starting off. Most people are somewhat close to and can get to a zoo for practicing with a scooter; I wouldn't let him do this alone. The zoo will more than likely only have 3 wheel scooters. Some people use the free scooter at the grocery stores to practice, but those are bigger and bulkier then one you would probably rent. Most say the grocery store scooters are harder to use than the regular ones.
All of us are different and some don't adjust very well using a scooter. My MIL had issues with using one at Disney. My mom could never handle using a scooter; she never even learned to drive. She's 90, now. Make sure he's comfortable and safe using a scooter.
I feel the wheelchair in the park is recommended. There are attractions that you can get the wheelchair right on the ride. This is not true of a scooter. It also takes some concentration to use a scooter all day or part of a day in the park. It's crowded and kids especially don't pay attention too well and they can dart out at you in front of the scooter. Getting on and off a scooter in his case may be harder then using a wheelchair especially for going to a restaurant to eat. Most restrooms are not too friendly to scooters, either.
I'm really not trying to scare you, but more I'm trying to prepare you. In most situations you should be just fine. My hubby loves scootering. It has allowed us to enjoy many more vacations.
We use Apple Scooter Rental, too.