Can one SH over needles? If so, does SH dair work? SH dair is an awesome counter to needles if it works, but I have no one to test with. I like SH dair because it does a ton of percent and forces techs at mid-percent. SH uair and fair are also obviously good and should be checked to see if they work [SH RAR uair can start combos very well]. This would help the MU slightly if we can [some Sheiks needle at point-blank as a get-off-me, since often people shield after it leading to grab, and also because close-range needles do more damage], but it's no deal-breaker if not. I apologize for asking here but I have no one to help me test [sorry].
Fsmash outranges her ftilt - if someone does an ftilt string but does one too many you can fsmash depending on the timing [and can fsmash it if they do it again trying to snuff out an aerial after you fall out].
I think it's about even - when I play Sheiks [including a few pretty good ones] I basically never get combo'd into bouncing fish [even off fair bouncing fish] so as long as you're wary of aerial needles, she'll struggle to KO [I live to about 160% when I don't get fsmashed (fair near the ledge starts to kill us then) and still usually to at least 120% otherwise]. For dthrow, I recommend basically ALWAYS doing double jump airdodge - it avoids uair AND Vanish if done correctly as far as I know [at least at percents where uair doesn't true combo - at some percents you just eat the uair and deal with it - but when I'm in Vanish range I'm not hit and uairs seem to miss me as well] - and at the percents where she can Vanish or uair she usually have to double jump for the uair, meaning you have decent time to figure out how to land. As far as onstage, I THINK Pika fair outranges hers when spaced correctly, but hers is faster, so it's a constant spacing battle [in the way Ike fair outranges Marth fair in Brawl, but Marth fair is much faster]. We both combo each other pretty well, although I think Pikachu is slightly better at comboing Sheik, but Pikachu's combos are also a little trickier. Pikachu may struggle to KO Sheik if you can't land those reads or punishes due to Sheik being so safe, but if they whiff a Bouncing Fish, usmash KOs around or before 100% if I'm not mistaken [her fsmash kills us slightly later on a whiffed smash, so be careful!]. I may be painting a picture suggesting Pikachu wins, but Pikachu's grounded tilts are simply outranged [dtilt can maybe contend with the range but I'm pretty sure Sheik is tied or has us beat], and Sheik ftilt is amazing. It doesn't shut us down, but it does everything Sheik wants it to do - control space, combo, low lag and fast startup, and even kills at like 180% (which sounds dumb, but with her combo ability, over 100% is not that difficult and over 130%, it means those stray fairs still slightly matter) [if you're living past 190% they either don't know or you're a god at not getting ftilted...]. Her pivot ftilt is also awesome, so be wary of approaching a Sheik who is running away.
ESAM mentioned that perfect pivot utilt beats Sheik fair if spaced well - I'm not nearly technical enough to do that with any consistency, but as time goes on this might tend to make Pikachu better in the MU if people can do that consistently.
We win the MU slightly with customs on - you shouldn't be getting hit by her side special two (gravity grenade?) [just airdodge and up+b if you're high enough, or get hit by it and hold down to tech the stage if you're that low - and onstage we're fast enough to where it should basically never connect - and that's ignoring shield] and penetrating needles don't shield break on their own, so just run around some if you accidentally shield a full stack of them from afar (I recommend SH/FH airdodge from afar and shield -> grab up close, since I think they're laggy enough to do that) [but be wary of 2111 - shielding burst grenade locks us in long enough for her to unload a stack of Penetrating needles, and that WILL cause a shield break!]. Meanwhile, Heavy Skull Bash is amazing.
This is just my thoughts. People can feel free to disagree, call me out, whatever - I'm more interested in getting the nitty-gritty of the MU down than being right here. I also know there's a lot I didn't discuss. For numbers, 50:50 customs off, 55:45 customs on favoring Pikachu.