You can damp with resistors maybe, drop a cap acrross the line somewhere, depends what sort of buzz it is, I gather it’s more a buzz than hum, probably a humming buzz, or buzzing hum.
I was thinking if the input impedance down the line is a bit high it may tend to have a bit more noise. Like I said though keeping the signal up/attenuation low at the source and reducing it downstream generally gives you better signal to noise, though this is not universally true in the case of impedance being less than optimal, especially with simple volume and tone control circuit arrangements sometimes.
There is one other possibility too, being that if the filtering/decoupling of some old or inadequate part of a power supply were, well I already said it…“inadequate”, then this may add to buzz or hum.
You could maybe try, I dunno, a 600 ohm resistor across the 1/4 inch plug ground-core, and if you can handle a bit of rolloff at your top end frequencies maybe try a capacitor across there, haven’t got a chart with me to suggest anything but reckon you could organize that.
Or try same arrangement down the chain a bit.