Not withstanding what Jaded Faith recommends, which I'm sure will be good, cold solder joints can act as rectifiers and actually demodulate or,
in English, extract the audio from a radio signal and add it to your audio signal. This will only work with an AM signal as you describe.
Your guitar is acting like an antenna. Does your guitar have active electronics?
You can use a a small value picofarad cap (5-10 picofarad) from various points in the guitar, any signal point to ground, you'll have to experiment,
to send any RF signal to ground. A small value like that won't affect any audio level signal. (you can't hear it.)
Another thing to check is proper shielding.
Hope this helps.