Can Sheik edgecancel the up-B fall without horizontal momentum just from the way her body (i.e. landing detection points or whatever) contorts as she falls from the initial poof?
Almost 100% positive that she cannot. As in if you do a grounded one to the edge exactly, you won't have enough momentum to actually cancel it, even if you are so close to the edge that any step forward will make you fall off afterward.
However, if you are in the air at all it is feasible that you can get enough from falling to slide off.
For this reason I am also pretty sure you can't do one backwards (as in up B downwards into the edge and fall off to grab the edge) if that is what you were planning. Edit: If you do one straight down and have it end RIGHT before you hit the ground and hold backwards you can slide off and grab the edge. From what I can tell the applications of that are useless, and
no platforms are high enough/positioned correctly to let you vanish through them and ledgecancel (would be a flashy OoS platform escape option if it were feasible, but alas. I think platform dropping would still be better anyways. Plus unless you do one straight down they turn you around and you would then be offstage with your back to the stage.)
Edit: Actually on stadium you can up B from the platforms on the neutral stage and the water stage and cancel it by going offstage, but of course the spacing isn't that easy. You can also do it on say, the top platform of BF to the lower ones or to the edge. In fact, the easiest way to do this at all is to get on the top platform of BF, roll/walk to the edge, take a step inwards then up B grounded straight out and hold towards the edge of the stage. You will go past the lower platforms, hit the ground and slide off if you do it correctly. It's a bit slow but great to understand the kind of landing spacing you need. If you take half a step farther you will cancel it on the edge of the lower platform instead. You can also do this on dreamland by being at the VERY edge of the top platform and going straight out. I think you can go from the bottom ones to the edge but whispy makes the risk way more than it should be for the reward. You can go from the top platform to the edge out of a dash if you up B at the absolute edge of the top platform. If you get the double explosion you did it too late.
In general for this, the higher up you are, the less precise you have to be as you will get more momentum when falling, but also the slower it will be since you have to fall.
Like I said, I may be wrong because these are kinda tricky to do, but I just spent 5 minutes on FD doing grounded ones into the ledge with no luck canceling them. Plus I am pretty sure that if you appear on the ground, you appear with no momentum, making the cancel impossible unless the up B ends with you barely still in the air.