Knight of lodis was a tactics ogre game no? I liked the game (though I do well with most tactics games) and can not recall the music being overly annoying, that might change if you are putting real time into it though.
Other than ones made for certain games then GBA sound hacking is usually focused around injection of new songs, and though sappy will tell you the locations of a lot of things it does still involve quite a bit of manual work after that. You might be able to inject silence and have it do what you want, however I would probably fiddle with the sound engine or track itself if I was doing it. Tinke and all the DS SDAT stuff was a fairly large change from all that came before that. Back on old consoles sound hacking was usually only after encoded video and assembly hacking (though it probably involved a bit of that as well) in terms of what people considered the difficult parts of ROM hacking, sappy made that slightly easier but not by that much.
Are you playing on a PC emulator or hardware/limited emulator? If it is on PC then you can often just disable sound channels as music and SFX may well be on different parts of it all.