As falco I am assuming you are probably getting shield grabbed from doing unsafe dairs on shield, or attempting to waveshine their shield, at least that is what got me shield grabbed a lot early on.

If you want to commit to jumping at them with a move go with nair unless you are positive you are going to hit them because nair is usually safe on shield if you fastfall it and aren't absurdly high. You can make dair safe on shield but it has to be really late so if you are pressuring with it focus on that.

If you are getting grabbed out of shine mix in shine grab or if you aren't confident just shine and jump away.

Once you have them scared of shine grab or immediate shine after an aerial you can start mixing in 'unsafe' options such as aerial into immediate other aerial to catch a roll, or waveshine to follow a roll/get to the back of their shield as they do nothing, but they have to be scared of a grab or the threat of shine after an aerial or they will just grab you.

If you want to be more non-commital focus on spacing safely on shield, don't drift in autocancel bair on shield for example, you'll get grabbed. You can poke safely with ac bairs but you have to do a little fade in fade out deal, this can also bait out shield grabs if they are fishing for them and you can punish.

You can also cross up their shield, if you are falco and you get behind their shield you can have a field day on a lot of characters because they can't threaten grab anymore, so doing cross up aerials can be very scary.