Man oh man- does this guy know his stuff or what!Technically not a travel set, even though it could be used as one, that's known as the Minute Man set in a Cigarette Case model. The minute man set was designed to be mounted on a bathroom wall or stood up on a counter top or in a medicine cabinet to hold the razor and new and used blades. The case was designed to hold the razor or it doubled as a cigarette holder, the cigarettes were held in place by the brass strips.
Very nice set for only $10! They were sold in the mid 20's.
I have an Ever-Ready version of basically the same set, though that came with a 1924-style. There'd be no mistaking its purpose from the packaging though.