First I'll say that in my opinion Sheik's chaingrab defines this matchup. If she is able to chaingrab you properly, you're going to be taking a lot of percent and end up offstage or being platform techchased. If she lands the fair techchase you'll be offstage anyways. Below a certain percent (somewhere around 20-30 I think) I'm pretty sure you can sometimes escape the chaingrab by nairing or jumping out. The other way to escape is by teching on a platform. Platform heights vary from stage to stage which is why I believe that this matchup in particular is heavily stage dependent. I always strike DL and BF and usually end up playing game 1 on FoD or FD.
I think DL is by far the worst stage in the matchup because the platforms are so high. She can CG you to upwards of 60% or so before you can tech a platform on this stage I think. Compare that to being able to tech on the inside of Yoshi's platforms at 11%. If you're getting chaingrabbed to that high a percent with platforms there anyways I think removing platforms from the matchup on FD is better than giving Sheik the ability to maneuver around your projectiles with platform movement. The width of the platforms on DL makes the uair techchasing less reliable, and the height of the top platform makes it more difficult to reach for uair chains. On FD there is no platform for Sheik to escape uair on, so it makes your punish game better while keeping hers about the same as on DL.
BF's platforms are a good height and width for techchasing on, but Sheik can still chaingrab you to a percent at which she can ftilt>fair you. I don't think you can tech the platforms here until the mid 40s at least. Another thing about this stage is that you can only hookshot the ledge safely (going for the "bowl" under the stage is very unsafe in general, but especially against a character as good at drop zone edgeguarding as Sheik), which means you can't mix up your aerial positioning for the hookshot. This makes it much easier for Sheik to aim her bair from the ledge when edgeguarding you. On other stages you can go lower and mess up her timing.
Sheik isn't very good coming down from above unless she is able to land some needles on you from a platform first. You can CC he late bair and late nair to probably around 35-45% or so, and that's all she will fall down with unless she has a read on your CC, then she might dair you or just empty hop down and grab you. You can shield grounded needles most of the time and can also use your Hylian Shield to block them if you don't have a bomb in hand. Be careful about shielding needles from the platform because the shield stun on fully charged needles is often enough to land next to you and combo into grab. If you get hit by that kind of needle you'll also usually get grabbed. Stay away from laggy commitments like approaching fairs (you can do retreating fairs if you don't get too obvious), dsmashes, and grabs. Focus on getting her percent up with bombs and boomerangs and then use those to combo or to get position below her. Jabs are good to keep her from just running up and grabbing you. Learning to DI dash attack, ftilt, fair, and dthrow are really important in this matchup. DI dash attack behind sheik as it sends you up and a little bit behind her. DI ftilt out and a little down to get as much distance as you can from her to make the fair harder. Fair you need to DI up and slightly out because it sends you out and slightly down. Just DIing straight up won't affect your trajectory at all. I'm not really sure what the best way to DI dthrow is. If the Sheik knows how to chaingrab it really isn't relevant which way you DI because she will always react and regrab you until you reach a platform unless she's bad.
Setups (some of these kill): You can shield grab Sheik's dsmash and her dash attack if the dash attack ends up in front of you. If she dash attacks through you you can up-B her OoS. Down-throw->upB is a solid setup. It works at a lot of percents but it's probably best around 85-105. You can also uthrow her and starting around 20% it becomes a 50-50 situation where she can jump out and then you're below her and she doesn't have a jump, or if she doesn't jump you can hit her with a move. You have to read it though until like 65% I think, at which point up-throw>uair works. If you go for an attack and she jumps she gets out for free and if your attack was laggy she can hit you back. If you don't go for an attack and try to wait out her jump she can just hit you on the way down. You can also try to bait Sheik into up-B OoS for kills by getting her to do a rising fair on your shield when you're on a platform. She will drift above you and you can just upB at that point and catch her falling into it.
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