When getting around the stage, you should be throwing out some serious lasers that force Pikachu to move away or above you. If Pikachu gets too close to you, you can try shining or starting a
pillar when you get the opportunity. The gimping off of stage is partly because Pikachu has really good edge-guarding options, so you just wanna stay away from getting off stage as much as possible. This is especially apparent since Pikachu has so many good options with keeping you off stage (f-tilt, u-air into u-air or n-air, d-air).
The best thing Falco can do is be either super campy with lasers and wait for Pikachu, or be aggressive as hell. All your hard work will come from being on neutral stage, as you don't want Pikachu to push you off and edge-guard you. Never give Pikachu the chance to get close to use and down-smash. If you do get down-smashed, it should be pretty easy to SDI out of it. You don't want to crouch-cancel it, obviously, as Pikachu will get more percents from you.
The reason why I say to use lasers, is because they limit Pikachu's already small range, forcing him to jump on you. Pikachu can become a literal canvas from here, so try you best to come up with something to punish Pikachu for coming towards you. You'll most likely have to learn to read well, since spotdodging nairs or incoming uairs can be super useful. Hope that helps.
