I don't like to kill anything unless I have to. I've had worst luck with intimidating the feral cats in the neighborhood than I have had with hawks. However, I don't have a lot of hawks in this area, one or two pairs at most (guessing one Coopers and one Redtail). I know that when I was in Kansas for a few months, it seemed like there were hawks everywhere, maybe a pair per 4 or 5 acres. So, I protect my flock the best that I can. I lose a chick here and there and maybe one of the smaller layers to hawks. But, I have dogs and cats that take more than any hawk does. Again, I use a scareman, some bling in the trees, occasionally a shot out of a .22 with snake shot (if it is accurate at 5 yards I'd be very surprised) to scare "things" away, bigger chickens that are less of a target, netting over my pens, bushes and low level trees to discourage the predators and give the chickens a place to hide and a rooster in every pen whose job it is to keep an eye out for danger. If the roo doesn't do his job, well, he ends up in the pot and the next roo gets himself a harem. Even with all of that, I still lose a few, but only a few, particularly the chicks and smaller hens.
Whether they were once "near extinct" or not red tails and Cooper's hawks now have the exact same conservation status as subway rats, look it up. They have the lowest status possible with regard to their numbers and if an "overprotected & thus overpopulated" status existed, that is what they would be. The law that protects them originated in 1916 and is still there only because nobody has made any real effort to update the species that may still need protection.
S.S.S. Do it without hesitation and most importantly without guilt. These killers are not endangered any more than the cockroach in your kitchen.