Check the plug end of the pickup. You should be able to unscrew the sleeve from the jack and visually inspect the cable solder ends. If any one of the ends look shoddy I would try resoldering it.
Usually a buzz sound indicates a broken or unstable ground in the cable. Since its hard wired into the pickup you may have it broken inside the pickup. With a little patience though, either problem can be fixed with new solder and/or a new cable.
Even if you require a new cable, it should be replaceable without getting a whole new pickup.
If you do take the chance of repairing it yourself, I highly recommend using a razor blade for easily getting the cable apart.