What a catch!!!
Now, in my collection I have a good number of razors which I've cleaned up and they look very presentable, but just recently I've been experimenting with a new de-tarnish routine which is giving my already good looking razor a really good shine!
Take a milk pan and line it with tin foil to about half way up. Pour in boiling water to about two thirds the way up and just as it comes up to a rolling boil, drop in a tablespoon of soda bicarb and a good pinch of salt.
Drop the razor in and boil it for about 10 minutes.
Let it run under cool water for a few minutes and you're done - any hard to get tarnish will have removed.
This routine is perfect for silver coating, but works equally well for all manner of vintage razors. I gather this is NOT good for gold plated and I would err on the cautions side for plastic and bakelite.
Lubricating, I'd say some Ballistol would do the trick. I tend to use a metal cleaner called De-Solv-It, which is a bit hard to come by, and that works as a nice second step where something like Peek and a duster is not needed. That cleans and lubricates. Ballistol should do you proud.