There are many rides that you can take a powerchair right on. In general, only one wheelchair can be on the ride at a time, but you can ride many things without having to transfer. Jungle Cruise, Tiki Room (show), Philharmagic (show), Small World, Winnie the Pooh, Carousel of Progress (show), Monsters Inc Laugh Floor (show), Buzz Lightyear, Hall of Presidents (show), Liberty Bell steamboat... and that is just Magic Kingdom. I do all these things without ever leaving my wheelchair!
There are a ton of things you can do without transferring in Epcot (and i suggest trying Soarin too - very gentle and a fairly easy transfer) too. Lots of shows which require no transfer (American Pavilion, Mexico, China, Canada, France all have shows).
I have very delicate joints and neck problems ranging from C5-C6 to S1... so I am a mess and I still manage to do all kinds of things.