So as a Falco who frequently plays against a Falcon you can:
- Roll out. This can obviously be punished but if you make it unpredictable it can be super handy.
- Grab. If the Falco always goes for late aerials into shine I'm pretty sure you can grab after the shine comes out. Grab can obviously be beaten by other things but you should never respond only in one way against an attentive opponent.
- WD oos. You said you need to work on this and you're right. It's a super important tactic for probably every character on the roster. You can wavedash away and then jab, grab, aerial, or just dash away depending on what they do and their spacing.
Other than that you can jump into an stomp, that seems to hit me once in a while. Don't spotdodge. If you wanna get really janky you can up b oos but that's just an idea, I don't think I've ever seen or experienced it so it probably sucks.
Keep in mind I don't know frame data behind this, these are just things that I've seen come out of Falcon to counter shield pressure. Also keep in mind there is no perfect shield pressure.
As far as advice goes to avoid shield pressure, most situations are set up with lasers. You can do a lot of things against lasers but I'm sure if there is a match up thread on the Falcon boards it is discussed there. Otherwise just do a lot of dashdances and movement to avoid having to put up your shield for other attacks.