Since I didn't see a reply, i figured I'd try and help a bit.
Handicapped Parking would be in the main parking garage, so the Valet parking would be closer to the park entrances.
As for Wheelchair availability, I can't comment since I don't personally have any experience or first hand knowledge. I can however say that usually parks would have a good supply onhand so the likelihood of not being able to get any sort of mobility device would be slim. I could however foresee a possible situation where if you were wanting an
ECV they may be out requiring a "traditional" chair......(do parks even still rent those?).
I'd also suspect that the process may be sped up if you are able to reserve online since they'd already have much of your informaiton available.
Other options or info from things I've seen/heard. While Valet is closer to the park gates, The Central "hub" between the 2 garages may also have some chairs available to rent. This would be closer to most of the garage handicapped parking than Valet would be to the front gates of the park.
Since you have a car, you may also be interested in checking on some of the ECV/Chair rental places servicing the orlando area. You would gain the advantage of not having to worry as much about the travel from your car to the park during your entire trip, and it may even end up being less expensive to rent for your entire stay than renting something at each individual park.
You may also want to hop over to the disABILITIES forum since I'm sure you'll be able to get a lot of additional information there from people who have more direct knowledge and may even be able to give you some additional tips to make your trip as hassle free and enjoyable as possible!