^what starship said. there's a sweetspot that the game keeps registering forward to run, but it's far enough down for the game to think you're holding down so it won't let you go off the ledge. once you find the spot on your joystick, it's not too hard. finding it can be a pain tho.
as far as moonwalk/stickywalk goes, i'm pretty sure anyone can do it. it's just a side-effect of physics. but the usefulness is dependent on character. like...bowser can wavedash, but that doesn't mean he should even bother. most characters' moonwalks are useless to the point of non-existence. off the top of my head, the only characters with noticeable/practical moonwalks are cfalcon, sonic, and mewtwo. i'm sure there're a few others tho.