This is the first time Archie is seen shaving. He is using an old style straight razor. These razors are designed to be kept and resharpened for a lifetime (or longer). In the past, Archie has come downstairs with bits of toilet paper on his face complaining about Edith using his razor and dulling it, and Mike joking about Archie trying to get "one last shave" out of it. Indicating that Archie uses a regular disposable blade.