You are distributing the music to other people, so this doesn’t look like personal use at all.
You can find music that is sold for exactly this purpose cheaply. (Similar to stock images that can be quite cheap). The seller probably knows how to combine this with open source.
Or you can modify your code so that it lets the user choose music on their computer, assuming that they have the right to play that music.
But also to keep in mind: If you create software including proprietary music, and manage to do this legally (fair use, private use, no profit or whatever arguments to use the music), and distribute everything under an "open source" license, then you give everyone permission to copy this as long as they follow the open source license. With the GPL license for example you claim that you give ME the right to copy everything, turn it into a commercial product, and sell it for $100 a copy, as long as I follow the GPL license. But whatever legal excuses you had to copy the music don't apply to me, so we have a legal problem.