Myself, and anybody I've played with, shakes their hand parallel to the neck. I've seen BB King live, and he does it that way, too.

Use the tip of your finger, placed so that you press perpendicular to the surface of the fretboard, and roll your fingertip rapidly back and forth between the frets.

Trying to shake your hand perpendicular to the neck, (across the fretboard), is likely to do some bizarre things to the pitch, especially if you're doing a bend at the same time.