Do like this:
Line a bowl with aluminium foil.
Pour a generous amount of ordinary baking soda into the bowl so that it covers the bottom.
Put the razor pieces in the bowl so that every piece is connected to the aluminium.
Pour a bit more baking soda upon it.
Pour boiling water upon it so that the whole razor is covered with water. That starts a reaction that's totally harmless and that's been used by house keepers and house wifes for more than a century. All the black oxidation reacts with the soda and goes back to is original state: pure silver.
When the water has cooled down to you can use your fingers to pick up the razor parts and you'll have a razor with as thick and shiny plating as it had the day it left the factory.
I posted a picture in this thread about a month ago with the last single ring I gave this treatment to. It was nearly as black as your razor.
Thanks polar! I'll try this when I get home with it in about a week. I'll get some pictures up after she cleaned up. Thank you for your help. I also noticed a hair line crack at the top of the handle. Seems like this is pretty common and not much to worry about.