Just my own opinion, but I dont' consider Van Halen to be a shredder.
Nor Satriani or Vai for tha matter.
When I hear the term 'shredder' I think of a guy I saw at a guitar competition once.
Everybody else was playing these complex 5 minute solos that included a variety of different styles. Really great stuff. Then he comes along and basically goes nuts on the guitar running around the stage, playing scales as fast as he could, flying his hair around with the lights flashing. Meantime he's missing notes and he's really sloppy cause he just wants to look like a 'rocker'.
All his friends are cheering him on and applauding, but every other guitar player in the audience is sitting there, laughing their heads off.