The repeating magazine safety razor from the 20's is like the bolt
action rifle of the bathroom - but I'm not sure how carbon steel blades
would have fared in the enclosed magazine once you get some water and
lather in it.
It seems like the idea of a multi-blade razor goes back a long time - this one from 1933 looks rather unwieldy to me.
An early - 1944 - patent for what we would call a cartridge razor today... showing that Gillette started thinking about renewing their vendor lock-in fairly early on. Disposing a cartridge with four razor sharp edges sounds... interesting.
This patent for a disposable razor from the 50's would at least have made a neat little travel razor - you could almost fit something this small in a wallet if you wanted to.