Yes, the signal from two core balanced cable (but is this configuration used?) would not be affected, but neither would that from single screened cable if the jack socket is only connected to the pickup. If other metalwork (like control mounting plates) were bonded to the sleeve connection of the socket this would make the set-up very suceptible to hum.
Presumably these are being offered at a bargain price. How did these cables get out of the factory? And are there any other potential manufacturing faults?
If they're otherwise ok, you could rewire the plugs, or fit new.