There is no way I would ever try to free a hawk that was trapped in my coop netting. That is just asking to get the and torn up by it. Have you ever got a look at their talons?
Unfortunately, the laws protecting birds of prey are quite clear on the subject of who is protected and it isn't the poultry or the owner of the poultry.
Best to keep chooks safely under cover if there is a winged predator problem around you. I look at it as being on the same line of logic as if we lived on a busy street and had a 2 year old child. You wouldn't let that child outside without supervision to play in the traffic would you? Of course not. You would have a fenced in yard for it to play in. No, chickens are not children but you get the general idea.
Yes, I would love to be able to free range my birds, but with problem predators like Hawks, Eagles, Owls, Fox, Coyotes, Raccoons and yes, even Cougar, the only way I could safely let our flock out was if I could find little AR's for them to carry slung around their necks.