I've been there many times as it's very local to me. There is a lot of walking but there is the road train and you can hop on and off that at various points in the park. They do have mobility scooters (or they did last time I went) but you'd probably need to book that in advance. Most of the enclosures can be viewed from the paths which are pretty level.
I've been many times, but not for a while now. I went with a disabled friend last time. As a badge holder he was able to drive round, don't know if that has changed now, though. If you struggle with walking, try Longleat instead, it's fun for all