Q: is it musically possible to modulate the vocals but not the backing track and have it sound ok, or will it always sound dissonant
A: if you want to raise the vocals but not the rest of the music, you would have to do it note by note. each note would move a different amount. you could just do it harmonically using mostly maj/min thirds and also 4ths, or better yet re-imagine the line entirely. but i'm not sure i understand the situation you are doing this for