To reduce buzzing, chokes are usually varnished or potted. You can get small volumes of varnish on ebay. Or you could try potting it with epoxy.
Don't know the geometry of the choke, but it can also help to space the choke off the PCB a little so the noise isn't conducted directly into the PCB which can act like a speaker.
You can also leave it out, the circuit will just send more noise onto the line.