The easiest thing to do would be to just open the in game options, go to the Sound tab, then lower the music volume to zero. That would disable all of the in game music, as technically it all should trigger a copyright strike given that it's all copyrighted.
Otherwise, if you want to be more specific with only disabling certain songs, you could use SIE and find the names to all of the songs that are copyrighted, then download a silent mp3 file, and plop in your SWG directory and rename it to the song file.
Example, to get rid of the "Star Wars Theme" in the intro video, make a silent mp3 at "music/intro.mp3" in your SWG directory. At least I think that's the file, it's not the main title screen, but the intro video. Either way, tracking down all of them will take a lot of time an effort. Hence I suggest just muting the in game music.