I've not seen that model of Silvertone amp before but it sounds like it would have been made by Danelectro, no?
I have a '65 Dano DM25 with the same Reverb, Tremolo, and Ground-Switch configuration that you describe.
Mine's also all original, including the 2 prong plug. I've never been concerned about it before, but now I'm wondering...I have been thinking about doing a long overdue clean up and perhaps replacing a few caps and maybe the tubes. If I should I replace the plug, doesn't the ground lug also need to be wired back to the chassis, or is it sufficient to have it in proximity to the power? Might not be a bad idea to replace the power cord altogether with a three-wire and integrated modern plug.
p.s. If you're looking for a schematic for your beast Schematic Heaven has a lot of info:
http://www.schematicheaven.com/bargainbin.htm