Can scabies live on razors?

Not likely: And you would see them. Easy enough to replace a razor if truly concerned. It sounds it is time for a visit to a dermatologist/skin doctor. They can help you with the area on your body that you are concerned about. Would also take with you any of your contacts you suspect may have similar issues. All needed to be treated or will just keep passing from one to another.

Scabies: Although scabies cannot lay eggs anywhere else but in their burrow, they can survive for 72 hours without a human host. Even after a human infestation is eradicated, personal items such as linens, clothing and sheets need to be washed in hot water and dried on hot air. Items that cannot be laundered may be stored in plastic containers for a few days.