I just purchased my first vintage gillette super speed. It's a 1957 model that is in good working order, but it needs a very good cleaning. I've never cleaned one of these up before so I'm looking for suggestions. I'm thinking of just using a dishwashing liquid and a toothbrush, then polishing it with a car wax. Will this work? I want to get it as close to new as I can get a 50+ old razor.