I would put some of the silver polish on a nail brush and have at it. Rinse and repeat as needed. That black is oxidation. If the polish can take it off the metal, it should get it off your hands! Otherwise Lava soap and time. Instead of polish, I use the aluminum foil and dishwasher powder in a non-reactive container, or a Blitz! cloth, which is AWESOME!
hand cleaner, like for auto motive work. sold in the dollar store, round small tub cost $1 each.its a thick gel type mixture, rub it on your hands work in it good let set for a few minutes 2-3 minutes wash off, will remove oil, grease, marker stains, ink, paint, you name it! Keep it handy for spot washing on your laubdry items, removing any stain on any thing it works better than any thing i have ever used. Even worked on red clay dirt that got in to the bottom of my daughters long white wedding gown, this stuff is awesome! try it.
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