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Imperial is a nice razor .... mineral oil will do between shaves. Mineral oil won't harm the scales. Dental floss soaked with oil might get between the blade and scales for further cleaning ..... the...

Assuming the razors are dull, but not dinged on the edge, I'd start building a new edge using your oiled hard Arkansas stone. (If there are dings, use the soft Arkansas stone until the dings...

First, wash the razors with dishwashing liquid and an old toothbrush. :? If it is just a light rust, an ordinary metal polish ought to remove the rust as well as the tarnish:
MAAS,
Metal-GLO,...