Pikachu is better against ZSS than Falco is. If you know this MU well you shouldn't have too much trouble against any ZSSs on your level
Jolts are good. FH jolts from the right distance, coupled with good aerial movement, are hard for ZSS to get in on, unless she starts running in before you shoot the jolt, so don't be predictable with them.
ZSS' dsmash is safe on shield, so you can't punish it directly but sometimes you can punish what she does afterwards if you're prepared for it. eg If you try to shieldgrab it, ZSS can just jab after the dsmash and it will hit you before you grab her, meaning that the ZSS might go for dsmash --> jab. If she goes for that, just shield the jab too, and then grab that XD
If she just runs away after the dsmash hits your shield you can't really punish that cause she2fast
If ZSS shields the landing hitbox of your dair, that's a free dsmash for her so be careful with that I guess. The ZSS you play against might not know that but at the very least he'll probably punish with a tilt.
When she's offstage, pay attention to how the ZSS recovers. If the ZSS usually downBs back onstage, hit her out of it with a dair. Now she's offstage again and she has no downB, so her only option is to tether (or jump if she still has her 2nd jump).
If the ZSS tethers with sideB, you can react to the sideB startup and go down there and clip her out of the tether with a sourspot nair (nair has a nice lingering hitbox so that's good). You don't really have to worry about ZSS edgeguarding you if you're recovering properly and edgeguarding her properly, cause it's too risky for her.
Her uair beats your dair (it beats every dair).
If she's gonna land with an aerial, run in and shield, and then you should be able to shieldgrab it most of the time if it was a nair. If she lands with bair, it'll work less often but it's still worth going for. Any other aerial is a terrible landing option against Pikachu.