I agree with SandraEllen. The cords that hold the hood in place also snug up the neckline. A zipper hardly seems necessary for a 3" opening.
However, if you really want one, use the 4" zipper. Sew it in (by hand) so the top of the teeth hit the neckline and just let the remaining inch hang beneath the opening. There is a way of shortening a (plastic, not metal) zipper by machine-stitching across the bottom and cutting away the excess, but I've never tried it.