John, the Classic Trains forum is a better place to post this kind of question. More of the people over there have a lot of old Lionel experience. We'd like to help here, too, but we just don't have the know-how.
I suspect the handles of the K-dubya are press-fit on to the shafts. They should come off by pulling, but I would be very careful. The plastic is probably a bit brittle with age by this time, and you wouldn't want to break it. If possible, clean around the shaft with a Q-tip, but leave the handles in place. There isn't much you can re-condition inside a Lionel transformer, anyway.
Oh, and thanks for making the big effort to bring an old train back to life. I switched to HO long ago, but back when that train was new, I was running Lionels of my own. I still have to smile every time I see one, and I'm sure your kids will too. Merry Christmas!
It takes an iron man to play with a toy iron horse.