Just follow the wiring instructions that come with the PUP and then connect the new hot to the old hot and new ground to old ground on the DP3T slide switch.
Its just like swapping shoelaces, simply take one out and put another in. There's only two wires you need to de-solder and re-solder so you cant mess it up badly or anything.
You have a 50% chance of wiring it backwards if you don't pay attention which will make the switching controls work backwards (it will still sound the same just the switches will be reversed) and you have a 50% chance of wiring it 100% correct.
Read the instructions and give it a go!