im not a master solderer but i dont think you can de solder unless you make it really hot then pull the wires apart which might do more damage than help. instead you should cut the wire, then solder on the new pickup. as far as tools:wire cutter (or you could try scissors), soldering iron, and solder, then you should be good. if its your first solder then i would have someone who knows how to help you so you dont screw it up.
My gear:
gibson sg
fender stratocaster
vox AD30
crybaby wah