Swapping 9 inch to 10 inch

Depends. Are they both the same rear? I'm assuming the 63 rear is a 7 1/4. If the 72 rear is also a 7 1/4 (same rear cover) the backing plates should swap. To remove the backing plates you have to remove the four nuts behind the axle, thru the access hole in each axle then pull the axle out. the backing plate is just sitting on the studs at this time and will come off after you disconnect the E-brake and brake line. You will probably need a axle puller to remove the axles. I'm sure someone else will chime in if parts will change from a rear as old as the 63.