I'm with Mark, I think the LED's power conditioning hardware (built into the base of the bulb) is sending some kind of interference up your wiring and you're hearing it in the switch itself.
Try cutting the ferrite choke knob off an unneeded computer cord, route out the cable from the middle of it, cut and splice your switch's wiring through that. If things improve, you may be on your way to fixing the problem. You might need to scope it to figure out exactly what frequency the PC system is generating so you can select the right kind of choke for your needs.
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Lead or follow. Either is fine.
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