I made my 1" mops from scrap (being inherently CHEAP).
I got some 1/2" dowel, some sheet foam from an old sofa cushion, and an old terrycloth towel.
I glued 1 wrap of foam to the end of the dowel with contact cement and cut/sewed a piece of towel to make a "sock" (closed on one end). The sock fits over the foam and is secured with a piece of string. To wash, just cut the string and slip the sock off.
It works really good. It is soft enough to swab the bore easily.
Did I mention it's CHEAP? :mrgreen: