ycz6 (who is beside me right now) says you can Haxdash on every stage. Obviously normal getup/roll/getup attack/maybe even ledgejump can be situationally good. You can probably do a normal getup or waveland -> shield, spotdodge, or maybe some fast move--dtilt, dsmash, jab, or upb--depending on what you think they'll try.
If they're close:
In addition to fairs, I like uairing onto the stage. Fair often leads into upb, whereas fair/uair can maybe lead to a fsmash towards the ledge if they do some funny DI / get confused (I probably try this too much and get punished for it; I also probably aerial off the edge too much in general when they're too far away to get hit, lol.) Ledgehop dair/nair seem useful only as punishes for upbing onto the stage, though dair has advantage on shield so it might be safe.
Things that probably aren't that good (better players, tell me if these are secretly viable): ledgehop straight up -> nair/uair -> regrab edge [if they're reaaaally close]? ledgehop -> bomb -> drift back off stage? Upb through them if there's a platform you can reach?
If they're a little ways off:
Ledgehop missile (or Hylian Lowrider if you can do it?) or charge shot (I try this too much as well)
You can always drop off -> regrab to wait for them to try something, as well.
Also, if you're grappling below the ledge, you can do walljump shenanigans (hold in toward the wall as you retract the grapple, then walljump): walljump -> upb, aerial, doublejump aerial, missile/reverse charge shot, or even bomb can be good mixups. And of course there are other grapple tricks too (rising grapple, grapple cancel, bomb canceling the grapple in NTSC) that you can use to further mix your opponent up.