Handloading has been around for over 250 years. Tumblers...not so much. In fact tumblers, specifically vibratory ones are relatively a new in the grand scheme of handloading. Most of us that have been doing it for awhile started without one. I have laundered brass, spun brass, wiped brass, dish washed brass, wooled brass and even left brass as is right from the chamber. Some brass does not lend itself to tumbling well at all. Anything with a .20 cal or smaller neck that has a shoulder, not a good tumble candidate. Anything with a 40 degree shoulder, not so good.
Dish soap, hot water, rinse and dry. Gets all the stuff off you need off. If you want pretty, either spin it in steel wool or tumble it in a vibratory.