For non-destructive, safe cleaning, isopropyl alcohol wipes work well. However, I'm a real fan of the "magic eraser" and suspect it would do a good job here, if used very gently - just try it on the base first

Otherwise, look into black vinyl dye (which you could potentially apply with a small paintbrush to the affected areas), which will bring it up like new. Auto stores or hobby stores sell it.

JB