I can attest, though, that barbers, at least barbers from a good while back, usually had a spare razor strap or two laying around, though.
Different note: I was talking to aurora last night, and told her, and will share here, that I own my grandfather's razor strap which was used, of course, to sharpen his razors, but was also, as I understand from his kids (my uncles and aunts) used for the disciplinary betterment of the clan, also.