I don't know. I don't even have an -educated- opinion on the matchup in general, let alone to say so for that stage lol.
Hang on DJ, ima edit some thoughts in here.
If I were to say that Sheik wins there, then I'd be saying that she could get around Falco's lasers similarly to the ways that she could on most other stages(which she can on longer parts of the stage like seal or something). I'd also say that, because there aren't any real "edges" for Falco to grab, Sheik would have an easier time gimping Falco there than on other stages. I'd also argue that Sheik could catch Falco because his low mobility is more likely to get intercepted at more points in the stage than if Fox were laser camping. There might even be a small part of the argument that could say that Sheik could even escape Falco's combos by hiding underneath something so that when he approached(which he would have to do at least once for a kill) he couldn't pop her up enough to get guaranteed moves.
Now, if I wanted to say that Falco wins there, I'd say something to the effect of "Falco can still see Sheik coming and move away. His jumps give him more vertical mobility so he can escape to higher parts of the stage(sudowoodo's branches, wooper, chikorita, weezing arguably, etc), and he can still forward B to a completely different part of the stage(which would counter any "but what about the Unknown?" arguments if the Falco knew his forward B spacing) so he could set up camping again."[I hate it when I use useless quotation marks] I'd also argue that the stun Falco's lasers give lessens the difference between Fox's and Falco's lasers(in terms of damage dealt per camping from a given spot vs a Sheik). Sheik has no "edges" to go to as well, so Falco could punish Sheik's recovery much harder, and there are also several opportunities to kill Sheik with a spike(many open places) or maybe even off the top(shines/shine to up-B).
There's probably more for both sides, and some obvious(and not so obvious) counterarguments here, but this is basically what I think about that matchup on Floats.