I've seen a Puma with the rubber missing. The shank was relieved in that area and would make it very difficult to shave with it. Sorry, the razor was not mine and I don't have access to it to get a picture. Just think if it as a rim w/o the tire. I don't know if you razor would have the same issue. To replace it Google "vulcanizing rubber". To repair it you may want to consider RTV.: Amazon.com: Permatex 81158 Black RTV Silicone- 3-Ounce: Automotive
As a Tool and Die Maker I have worked with both. It's too much detail for me to post but the info is available on line with some searching.