Sorry, just to clear something up, was this wire you're using originally in the guitar? It sounds like it has two conductors and the copper wire is a shield.
You really need
three conductors - two to connect the outer lugs of the switch to the two volume controls, and one to connect the two middle lugs of the switch (bent together and soldered) to the jack socket. The copper shield could then be used to connect the ground lug of the switch (the fatter one in the middle) to ground on the back of a pot or on the jack.
Since you don't have a third conductor, your copper shield
could be used to take the signal from the middle lug(s) of the switch to the "hot" connection of the jack. But then:
1. There's no wire grounding the body of the switch itself.
2. You'd need an extra wire to connect the ground lug of the jack (to the back of a pot)
3. If the bare copper wire comes into contact with the back of a pot (or pretty much anything really), it'll short out the signal. So you need to cover all the exposed copper wire with some heat-shrink tubing or tape or something.
I think you'd be best off with some new wire.
There's an excellent thread here, where Jonesy76 used vintage-style braided wire to rewire his 335:
http://bareknucklepickups.co.uk/forum/viewtopic.php?t=10301&highlight=And here's a Seymour Duncan diagram:
http://www.seymourduncan.com/support/wiring-diagrams/schematics.php?schematic=2h_2v_2t_3w