My previous post re clean-shaven Romans prompted questions re the technology used to shave in that era. This video (via Time Travelling) shows a primitive skills educator making his own blade by knapping some obsidian, then shaving with it.
These scanning EMs [credit: William A. Haviland] show that an obsidian blade is as sharp as, and smoother than, a modern steel scalpel.
Obsidian knives have been developed in modern times, but I suspect they could never be employed internally because of their intrinsic brittleness.
Finally, for completeness, Razorland has a gallery of primitive razors (bronze, iron, and copper) from a variety of early cultures.