Put on disposable gloves. Yes, WD40, put all in a folded rag, roll them back and forth in the rag tube. Throw the rag away. Wash your hands thoroughly. The white powder is lead oxide, it is very toxic and easily absorbed. IF I am getting fancy I tumble may cast balls with graphite. It makes them pretty, removes the sprue and slows oxidation.I'm with Scota. This works great!
For what's worth, I don't seem to have that problem even though I have some cast bullets and round balls which are more than a few years old. I spray them down with WD40 [ stored in plastic peanut butter jars ] after casting .