Fill your pockets so there's no room for anything else, preferably with any items you can consume, equip, or toss. Ask K.K. Slider to play a song and if you do not like it, K.K. will not give you a bootleg and you can listen to another song. If you still don't like it, toss, eat, equip, etc. an item to make room and then request the song that you wanted.