If you can find one of the old Herters shell drill adapters, it's a three part shell holder (a shell "chuck" would be more accurate) on one end, & a short hex shaft to fit an electric drill on the other (RCBS made one for a while too).
Flitz, "0000" wool, or white rubbing compound (Like Troy said - NO ammonia) will do exactly what you want. They not only take 1/10 the time to do, but look 10 times better. The one Lee has out now is CHEAP, & would be perfect if you can hold a complete cartridge (with the primer) in it.
Course you could swipe 3" of your dad's tubing, put it on the cartridge base, & gently chuck it in a 1/2" drill,,,,, this really does work nice - the things'll look a lot better than the day they were made, incredibly shiny! "0" wool, or 600 W&D gives a very fine machined look, but still very shiny.