Tinwhistler, speaking from a little experience, I would say that if you can plug in even a very cheap microphone into your boombox (the kind that used to come with cassette recorders before the built-in condenser mikes were invented) you will get a much cleaner recording. These mikes are probably still available at Radio Shack for around $5 - $10. The key is whether your boombox has a microphone input socket.

Otherwise, you'll need to be in a very quiet room with good acoustics to get a decent recording.