That patina actually looks pretty nice on a WW2 zinc Nazi coin. I say leave it alone, but a mineral oil soak to remove surface grime should be safe enough to do without causing any harm, provided you're gentle when you wipe the oil off with a soft cloth or paper towel. I do not like olive oil. It is mildly acidic and leaves a sticky residue. In my experience, mineral oil is preferable and I actually like petroleum jelly (Vaseline), since it's less runny and messy for a dab on/wipe off application. And Vaseline or mineral oil might actually help preserve the coin in its original state, but would be less permanent than lacquer, which old-school collectors of yesteryear used. Lacquering is a no-no now. I would avoid any other kind of "cleaning", by mechanical or chemical means.
Zinc is a real pain to deal with. It's very reactive with air in a moist environment. The face value and mint mark (small letter at the bottom center) are on the reverse. IMO leave it as it is but store it well. Probably not a lot of value.
Yup, of all the metals you might try and cle...uh...conserve, zinc is by far the most problematic. It is a moderately soft reactive metal, so a light coating of mineral oil and some light brushing with a toothbrush won't hurt.
The coin is zinc? Don't even try to touch it. It appears rather attractive now. Zinc is absolutely one of the most difficult coinage metals to work with - nearly everything reacts with it, and nearly every reaction seems to ruin the surfaces or eye appeal. Your coin appears stable and attractive. Leave it that way. Zinc and aluminum..... just don't even try to do anything with these metals.
