I would solder a short piece of insulated wire to the bare mesh of the braided wire first. That wire should go where the black one of your old pickup was. The inner conductor should go where the blue one was.
Check the following: select the bridge pickup and touch a piece of metal. Does it hum more or does it get quieter? If it hums more, swap the wires of the bridge pickup, i.e. the one soldered to the outside braid should go where the blue was and the inner conductor should go where the black was.
If it gets quieter, fine - leave it as is.
Select both pickups - are they out of phase (i.e. is the sound very bright and thin)? If yes and it bothers you, swap the connections of the neck pickup.
Good luck,
Stephan
