There might be a way around it that I'm not aware of - but it's a bad idea to move *programs* to an external hard drive. Programs usually register their location with the Windows registry - I'm really not sure how this will work with an external drive - my immediate thought is that it's not a very good idea.
Your music however, mp3/wav/ogg or otherwise can just be drag and dropped to the new hard disk - you'll just need to point your jukebox program at the new location, and any library setup you may have for your music may be disrupted by this move and may need to be rebuilt. An inconvenience, but one you'll get over I'm sure.
Give that your music is likely to take up several hundred, if not thousand times more space than your music program, this should solve your space problem on your internal drive.