I like to use 3M bristle discs (like sand paper, start with higher grit and work down to fine) with a flexshaft. Then tumble.
If you tumble without removing scratches first, you will end up with shiny scratches. :-) (I learned this from experience.)
If I have handstamped something and want to oxidize letters, I do all the above including tumbling, then use silver black on lettering with a Qtip to minimize overrun, wipe with a polish pad, then reshine with finest green disc that doesn't take black off.