I doubt Charity Shops would sell them, but I have seen Hospices on eBay selling razors. You can always ask the Managers to set aside shaving equipment that gets donated and offer a good donation yourself for them.
Back when I used to dole out those charity bin liners and collect in a white van, we'd typically take a long wheel base transit to the brim every day. From that I would guess 2/3 would go straight out to the "rag man" and all electricals were put aside for another service to collect. Maybe only a quarter of the haul would get into the shop. I don't recall ever happening upon shaving equipment back then ... it was 25 years ago. I remember at the time, some charities like Oxfam had recruited in electrical specialists and they'd have "Superstores" in some cities with furniture floors and electrical sections. No idea what it's like today, but behind the scenes sorting put only the best out in the actual shop and everything else was moved on as bulk to specialist services.