Power shielding is super difficult, possibly more so with DK than other characters. It should be easier to do if your back is facing him. It's not the end all be all though if you can't do it.
Falco lasers do way more hitstun and put you in a worse situation if you get hit whilst you're in the air. Although it's tempting to jump over them and go for bairs, he might be expecting you to do this so he can punish. Most of the time, he will win trades in the air because of his disjoints.
A lot of the time, it's much better to just get hit by them whilst you're on the ground, then wavedash/roll to avoid the follow up. Or simply tank it and move closer towards him. Just make sure you don't get hit whilst in the air, since you take the hitstun there and if you need to land, you get time in the air where you can't get a bair out because you're facing him, and then you take the 5 frames landing lag too.
I find it can be really good to crouch cancel them, then go for a dtilt or an ftilt. Remember that spacies are super hard to grab in neutral unless they miss space an aerial or something. However your ftilt can cause a tech chase at about 55% onwards, which can lead into a grab or a giant punch.
In this matchup I'd say just don't get greedy and expect to have your momentum stopped a bit by lasers quite often. It's worth mentioning that your first two frames of the giant punch have invincibility, meaning that if you time it right, you will go through the laser and hit him. Because of this, whilst running away from his pressure, try to charge as much as possible.
With the same theory, aerial up b can be very useful to get through them if he's very close, as it has more generous invincibility than the grounded version. He'd also be coming at you from a horizontal angle, so the grounded version strong hit won't be as likely to hit. Also, the aerial version has invincible arms, which can let you get through the lasers and hit him if you're lucky (they don't cover him all the time). You might not land in time for the tech chase, but you'd take back the stage control.
I'd say that charge cancelling to turn around or being able to do a quick pivot into a hop is super important in this matchup, as the lasers are going to be turning you around a lot. You need to be good at switching directions to approach as quickly as possible.
I used to think this was one of DK's worst matchups and I was considering making a secondary for it, but I've started to take games off decent Falcos now. Icies now has that honour for me.
Edit: If he ever double lasers from ledge, you can up B to go through the lasers and kill him. If you have any method of practicing this, try it. Will stop working against people that know the matchup, but so many Falcos do this.
Also I play PAL so I can spam up B without risking losing my charge punch, but I still think it's worth losing the punch over to win the neutral game.