How about acrylic paints, specifically hobby and model paints? Possibly with a non-etching primer?
Silver itself is quite non-reactive. The etching is what you want to avoid, so I guess "non-etching" is a keyword to use.
There are model car paints that really have the same look and feel as automotive paints, but you should verify they're okay to use on metals as well as plastics; the primer is likely different for the two. (Lots of people restore old metal toys, so hobby people are likely to know about this stuff. Just mention the silver is plated, no need to mention electronics.) I'd specifically look at the acrylic ones.
Oh, and if you want to protect whatever is under the paint, consider using a lacquer layer. (Exactly what kind would be good for a plated surface, I don't know, but hobby paint people do; they used to use that kind of stuff a lot when they still made toys out of metal, and they're quite expensive and often restored today.)