The strategy I've found most effective for fighting against ICs, is to take roughly 50 damage in upairs before you start doing any kind of fighting. After that you can safely split up the Ice climbers without fear of being solo popo chain grabbed.
What we can do
Needle's are a lot more usefull in this MU than they should be, if you catch them desynching that's free needle damage, its also a free dash attack if you're within range. Dash attack is good if you are above 50 percent because it puts nana in the air, and if you hit both climbers it often hits them in different directions allowing you to capitalize. Bair is an amazing aerial tool for keeping them separated. if you can take their double jump away from them offstage just sit on the ledge, and at least nana will die. Our up-tilt goes through their dair, don't ask why it just does. f-tilt is also really good if you catch at around 20-30 percent, you'll get them both in there for a decent amount of time and if you finish with a reverse up-tilt(Like if you're facing left when you're f-tilting, you turn around and face right when you do you're up-tilt) it knocks them in different directions. GR->Dacus is guaranteed on popo( and I assume nana, never been in a situation where i could test that out in game)so if you get them decently separated at around 85ish, just grab popo. Sheik's grabs and throws are really fast, so it becomes a pretty good option unless they're expecting it. Never up-smash unless you're sure that you'll hit.
What they can do
We have no options against uair if we are above them. Unlike Pikachu whose upair we can trade d-smash with. IC's upair is too disjointed. Desynched Ice Blocks under a platform is something we can do nothing about without significant risk of being grabbed. Pivot grabs stuff out any approach we have, and cover landings pretty strongly.
What we can do about those
We have no options against uair if we are above them.-
If the ICs is bad, they won;t know that SH upair pokes without going above the platform, if you're playing one of those, just punish them once they over shoot, no hard punishes, just small damage until roughly tiltable percents... If they know/are good, you can either run to another platform in teh hopes that they'll chase and leave themselves open, try to run off the platform and bair... vanish glide off of a platform in hopes that they'll get too close, vanish where you are standing in hopes they jump up too soon and get blown up, b boost off of a platform and upon landing do a grounded b-reverse a needle throw. None of these options are guaranteed, but they're the only ones I've ever thought of and had work.
Desynched Ice Blocks under a platform is something we can do nothing about without significant risk of being grabbed.
Don't let them get into this position in the first place, if you see them desynching throw any needles you may have. If they have the percent lead and they get under a platform and do this, well lol that sucks. You can try and bait them out of it, or get some fancy bair landing gimmick, maybe try some fancy chain works or a vanish play. We don't have the tools needed to deal with this without a horrible risk/reward if they do it correctly.
Pivot grabs stuff out any approach we have, and cover landings pretty strongly.
Well don't approach obviously, if you can bait a pivot grab, you can punish it with needles, dash attack, dash grab and depending on how close you are f-tilt or d-tilt.
As for stages I personally only like the MU on Battle Field and Lylat, Pokemon Stadium Melee is a stage I'm also willing to play the MU on. I haven't ever tried it before but Pokemon stadium 2 is another stage I'd like to try it on, the Ice/wind/metal transformations may screw up chain grabs. If you aren't afraid of a pocket mk then you can try rainbow or Brinstar. I guess SV would be the next best option. But I hate SV, i think its Sheik's 3rd worst starter on the current list, in the MU its probably her 4th worst stage(lol FD).... and where you're most likely going to start the set. As I've said before i think you need multiple platforms, SV's 1 moving platform while somewhat helpful is not nearly as useful as the 3 on BF, or the 2 to 3(depending on the transformation) on pokemon stadium. The SV platform is also platform cancellable, and when it move all the way to the side you're in such a dangerous position. Like if they just jump up there and land an f-smash all of a sudden you;re trying to recover, the platform is going to begin moving away from you so you'll be forced to vanish, if they're smart nana will be sitting on the ledge and you''l be forced onto the stage where popo will grab you. And even if you were to somehow reverse that situation, and knock them off, unless they're at really high percents they can just recover low and theres no issue.