Hello 131 and All: Yeah a small transistor radio will work, but you have to wrap it up in aluminum foil and allow a small opening near the antenna so that it only picks up noise from a select direction, instead of all directions, which will send you inside playing with your spit!.
The Op has not told us yet if removing the antenna coax from radio while receiving the noise, goes away or stays. I am thinking the noise is being radiated into the air being picked by the antenna and radio. I am betting its being radiated into the air. So a inline power wiring filter won't work.
Another problem hear I believe is the Op has never probed around looking for noise, so this is new and probably not understood by him. Not his fault.
Trouble shooting EMI or RFI ( Electromagnetic Interference / Radio Frequency Interference ) even by professionals is not easy sending most walk away frustrated and pissed off at the world. Resulting in walking away needing a totty or two. I know, I've done it many many times. If you keep at you will fine the source of the noise being radiated, and shield the wiring or install snap on ferrite cores over the source wiring. Again good luck.
Jay in the Great Mojave Desert