How does sheik beat peach i don't even know.
Space bairs, throw needles, and grab a bunch, she can crouch cancel dsmash basically the entire rest of your moveset until she gets pretty high percent. Get mad damage off of any grab (fairly easy, but I or someone else can go into more detail if you need it), and when you get her offstage edgeguard her with bair and/or needles depending on height (or you could be cool like drephen and walljump fairs from the edge

).
If she gets you off the stage recover to the edge every time, once you are on the ledge peach is completely incapable of touching you. If she edgehogs just go to a platform, she's usually too slow to get there in time unless she predicts it well in advance. If you can't get to a platform (or it's FD) 90% of the time peach is gonna get off the edge and try to dsmash you back out again, so crouch cancel the first hit of that to get sent back into the stage instead.
Other than that basically just don't get greedy. Peach is pretty good at messing up most of your approaches (usually with cc downsmash), but since she's slow as balls it's not too difficult for you to just stay away and wait for her to make a mistake that you can punish. Once you're in you can mess her up pretty bad, so just wait for the safe opportunities to do so.
EDIT: Has hiroshi gotten better at playing vs peach? He used to complain about the matchup all the time.
Also, ask exarch. He knows that matchup backwards and forwards, with either character. He and hozart are where I got most of my wisdom for that match.