If we're talking about composers that have inspired my sound design, I'd have to reach back a little further and say Harry Partch and John Cage for their sheer inventiveness in the acoustic world.
And don't forget Pierre Schaeffer and the developers of Musique Concrete who were pushing the boundaries of sound manipulation well before most of us were born.
And Ennio Morricone...who created new and interesting sounds that by layering instruments together, not to mention a new genre of "western." Also a master at sonic storytelling.
And, of course, the Beach Boys, the Beatles, and Hendrix who pushed pop music and multi-track recording to a new level.