Source: In common use
The kozuka (小柄) refers to the handle of a small utility knife that is carried in the scabbard of Japanese swords and daggers. It was used for whatever the main blade was too big or too precious for. The whole knife is called kogatana (小刀), but in collector's circles, the whole is often called kozuka. Like with Japanese sword guards, tsuba, there is quite a collecting culture around the handles alone.
A nice kozuka with nanban style decoration.
Sold by Mandarin Mansion in 2017.
They were typically worn on the side of the scabbard facing the body when the sword was worn, and part of their hilts would stick through a hole in the tsuba (鐔) or "guard" called kozuka-hitsu-ana (小柄櫃孔).