You can't reverse the wiring at the control cavity end because it's single-conductor braided shield wire - if you flip it, the shield becomes hot, and so does the pickup baseplate, polepieces etc - so you get a huge amount of noise, and even worse if you touch the polepieces.
You can reverse it at the coil though - the bobbin has two thin lead wires, one of which is soldered to the center core of the shielded wire, the other to the baseplate. If you flip these you reverse the phase too.
You can do either the magnet or the coil wires, or if the guitar is in phase anyway, you can do both and make the middle position hum-cancelling. If it's out of phase, and you need to flip one, you can decide if you want the result hum-cancelling or not - if it was out-of-phase and hum-cancelling before, and you want it to stay that way, flip the magnet. If it was out-of-phase and not hum-cancelling, but you want it to be, flip the coil. (This only applies to the middle switch position BTW.)