A little oxidation of the exposed lead will not hurt anything.
That is lead oxide that you see. There is no way to "remove" it chemically. It can be scraped off, but completely unnecessary and not recommended. It is this oxide that is the poisonous stuff though, much more so than metallic lead simply on the basis that it is so much more easily flaked off and ingested or inhaled when scraping, buffing or griding it off.
However...
A bit of oxidation will not hurt anything at all, so long as it is left there. I wouldn't let kids put it in their mouths, but it likely wouldn't hurt them too bad, until they bit a primer. (I did carry some non-copperplated .22 Shorts in my mouth between my teeth when I was a kid when out hunting. I think I'm still normal?!?
) What if I had swallowed one? Would I have passed it like a penny?
The only time that you should worry about lead oxidation is...on ammunition that dates to the time of the civil war where the oxidation has actually loosened the bullet from the case and may not allow it to chamber in a firearm.
Of course, those rounds would likely be more collectible than useful as ammunition.
My two-cents worth.