My, there's a name from the past!
I'd say it depends on the razor: brass, stainless steel or aluminum can be scrubbed or treated pretty much as you please. It's the plated pot-metal you have to be careful with, as the plating is easily damaged. If you are simply cleaning your own razor, I'd say a soft toothbrush and detergent would do. If it's one you've bought used and you want it sterilised, I would do the physical cleaning to remove debris with the toothbush and detergent and then soak it for 24 hours in something capable of killing both bacteria and viruses. Lacking Barbicide or other proper agent, Lysol or dilute bleach should do it. Vinegar will not. Alcohol can kill bacteria but has real difficulty against viruses. None of these things can be relied on unless the razor is physically clean first, as bits of debris make great hiding places for bugs and will let them survive.
Scissors and forceps I used in the office would be scrubbed with a brush, boiled in a sterilizer for an hour, then stored under Cidex till next use. The surface soon corroded and they had to be replaced as soon as that happened. Dry steam in an autoclave doesn't have that effect, but it would also detach nickel plating. Maybe Barbicide will turn out to be a bargain after all!