Danny
I recall that, about '60, Wilkinsons put a very clever thing on the market (I forget what they called it). Here a shallow rectangular case (perhaps 6in x 3) had a section of leather razor strop fixed into the bottom. A section of "cut-throat" razor (some 2in wide) was fitted into a handle which rode in side tracks to and fro, at exactly the right clearance for the blade to "flip-flop" on the strop..... Worked like a dream....... £2/2/0, I think
You're not confusing it with a Rolls Razor? I bought one of these self-sharpening razors from the "Edinburgh Castle" gift shop as I was on my way to 5FTS (RAF Thornhill) in Rhodesia in 1951 - it worked superbly well. The idea was to place a normal safety razor blade in the Rolls and it automatically re-sharpened the blade against the leather stop - this could be done dozens of times and saved a fortune in not having to buy replacement blades from Gillette or whoever.