Just to confirm, does your car still have the tapered axles? Up to '64 were fitted with these, it's commonplace for people to change these for '65-69 B-body rear ends, which are a little wider than the '62 model.
The tapered axles have a nut on the end which retains the hub on its taper. They are more difficult to deal with when it's time to service rear brakes, but they can be altered to overcome this.