Sundial Wire has discovered that self-fusing silicone tape is a wonderful means of taming the fraying ends of cloth-covered electrical wire.
Your wire can go from this
with the application of this tape. The tape adds minimally to the diameter of the wire.
This tape is 1/4" wide and is self-adhering. There is no adhesive on the tape. It is applied by holding it on the wire, stretching it,
and wrapping the tape around itself.