I would avoid using lasers in this matchup as fox. The only reason I see to use lasers is to get your opponent to be forced to go offensive, and since he has better lasers, you can't accomplish that in this matchup.
When Falco gets room he has the advantage. So your job as fox is never let him breathe. You need to constantly be applying the pressure. When you knock him down you cannot let him get back up without getting hit again. Once you lose him, and he has room to start lasers, he regains the advantage.
Also don't use the shine to reflect lasers. It's tempting, but never works out in your favor simply cuz the shine stun never allows you to capitalize. Also if the falco shines back the laser just bounces around and breaks fox's shield.
Your tech skill looks really good, and your tech chasing was good on land but not as strong when he was on platforms. If you throw him on, there is enough time to jump on an follow. If theres not enough time to get on and follow, I would use dair grab. Good DI, combos were decent but remember that good combos are the ones that get him off the stage, not just simply in the air with percent racked up. You may wanna try workin on a chaingrab, although its not essential.
I think you could use some work with edgegaurding, but it wasn't bad. I think its more reliable to stay on the ledge, make falco lose his double jump (usually knock them outta their forward B) than shine spike. Going out is kinda risky and not as reliable.
I worry about your recovery choice...You were trying to drop down and get under the stage and than Up B. He did punish correctly once by ledgehop Dair'ing you. I know that from above falco can shoot lasers and knock you down, but its worth a shot. If you get knocked down, than go for the up B and try and tech. A good trick is forward b/up B right where he can SHL you, get hit by the laser and than immediately foward B again, and this time you will be at the level where you will grab the ledge. Most falcos will not expect this, and its hard to punish unless you are ready for it.
I would definitely avoid double jump Nair like silent wolf said. In fact, the falling with Nair is a bit over-rated on falco since he can always Utilt through. the only thing you can really get him with if he is careful enough is your shine. But shine allows tech-chasing, so thats not so bad.
This machup sucks, but ya do what you can. Nice fox overall.
Edit: This is JFox, sorry wrong account.