Yeah I'm with the others. It's like thinking "Man I hate this line of dialogue, I wish I could remove it" The answer to if you want to remove a song from a scene is become a modder. As for lowering the BGM, sadly there's no shortcut to do it, however there IS a shortcut into the options, and that is the c button, so you will have to deal with the immersion breaker of the config menu.
Now I'm curous, what song are you wanting to mute (is it an H scene song)?