Disconnect the pickup from the pot first, then for 4 core wiring, just take the red to the tip tab and the black & screen to the centre tab. Make sure the green and white are soldered together.
For 2 core, the centre wire goes to the tip tab and the screen to the centre tab.
if you don't have a spare jack socket, you can do it with either a lead with a jack at one end, and just wire at the other (when you are doing a lot this is the quickest way, I have one with aligator clips to help me check pickups before I put them in), or you can tape the wires to the jack itself (the screen goes to the barrel and the live to the tip).
This will bypass all the electronics in the guitar.