D'oh! I just realized my previous post was useless, since you meant you wanted to listen to music on your computer. I thought you meant you wanted to listen to music like from a CD or something and I'm like, "well, duh, just turn off your computer volume and listen obviously". Silly me...
If I knew how TSC files are encoded, I could write a program to replace all instances of <CMUxxxx to <CMU0000, and then you can just reshack a blank org into the title screen music, but I don't. Though I do have the source code for CE, so I could maybe figure it out from that, except that I will fail a class if I don't get right back to work on this huge project when I get home.
Secretly, there's a piece of Windows called "svchost.exe" and if you open the music you want to play, terminate svchost.exe using the task manager, and then open cave story, the audio won't play in cave story (unfortunately, this includes sound effects, not just music, and terminating svchost.exe also causes some bizarre graphical glitches to Windows). Wow, I never thought I'd actually find a practical use for the horrible design of Windows...
The tl;dr version: replace all <CMU with <CMU0000 and change the title screen music to a blank org.