Well first thing to clarify is that:
Brawl Sheik =/= Melee Sheik
They play quite differently despite the appearance of her moves. Pikachu players tend to utilize the following moves against Sheik:
- Defensive D-Smashes (Multiple hits and pulls you in)
- Spaced F-Smashes (To prevent shield grabbing and attacks out of shield)
- Thunder edge-guarding
- QAC (Quick-Attack Cancelling, using his Up-B to quickly move around the stage and sets up for unexpected attacks)
- F-Throw, D-Throw Chain Grabs (0-60% for D-Throw, 0-70% for F-Throw)
Sheik should rely on good spacing and needles to give her the advantage in the matchup. B-Air approaches and spaced F-Tilts should keep you at a safe range from his D-Smash and Chain Grabs. Pikachu can be F-Tilt locked at low percents, so use this to rack up quick damage. Try to get Pikachu up into the air, as this will give you a chance to exploit the lag on most of his aerials. Sheik's aerial game + U-Tilt will give you a good edge against an air-borne Pika.
If the Pikachu is playing aggresively, wait for an opening to shield-grab or D-Smash to get him into the air. Also, try not to stay too far from Pikachu to minimize his camping, keep the pressure on him. If he uses Thunder, air-dodge to avoid it if you are above him; if its used for edge-guarding, use your tether recovery to avoid being hit or make use of Vanish's invincibility frames (right before and during the explosion). Thunder's hitbox stays out relatively long, so make sure you don't air-dodge or Vanish thru it too early.
Lastly, to kill Pikachu, edge-guarding is your best bet. Use your needles and F-Air/N-Air to pressure his recovery and force him to either sweetspot the edge (not that easy for Pika) or leave himself open by landing on the stage. Don't be overzealous with the gimping. A botched Pika recovery = easy D-Smash by the edge for KO. If you can't seem to get him to the edge, be patient or go for a surprise Vanish KO.
So the take home message:
- Utilize your range.
- Keep Pikachu in the air.
- Pressure with spaced F-Tilts, B-Airs, and Needles.
- Don't stay too close (Chain grabs) and don't stay too far (Thundershock camping).
- Pressure Pika's recovery and act accordingly.
The match-up won't be a landslide win for Sheik (definitely not like Melee Sheik vs. Melee Pika), but you should be able to win with a reasonable lead if played correctly.
Hope that helps! Feel free to shoot any extra questions or provide any input.