As I mentioned previously, I saw this idea on My Sewing Machine Addiction (http://mysewingmachineaddiction.blogspot.com/). She made her own ring connectors from the end of the wire. I thought I would try it.
First I scored the insulation between the two wires:
And stripped off that much insulation:
I understand that shrink wrap is not great protection if you need it for abrasion protection. I think in this application it should be fine.