Having those pickups re-wound won't fix the hum; it's a problem inherent in all single coil pickups. Those pickups look to be very close to the standard J shape & size, I'll bet you could get a replacement J-pup to fit under those covers with some careful trimming/shaping of the corners with a file or dremel tool.
Having the pickups re-wound could increase the output, but that will change the tone too. If hum is starting to be a problem I would check the grounds and shielding with an ohm meter.
"I have no actual information, just what the salesman told me."