Ugh! I know they have to eat something, but not my chickens! I have six cats & that's why I don't keep any little caged animals in the house; just doesn't seem right to have a predator staring at them all day, seems like they'd get the animal version of PTSD! Is it feasible to put a tarp over the top of the run for awhile? Maybe your girls will be ok if they can't see Mr. Hawk. And maybe Mr. Hawk will get the idea if he can't see them, either.
We free-ranged our hens until recently, when we lost our first chicken. We think it wandered alone out back behind the horses' stalls & got caught by a coyote. It had rained the day before & there were clear big paw prints in the mud among the gazillion feathers. We have lots of hawks around here, too. I've heard that a hawk won't take a full grown big hen over 6 lbs or so, as they can't fly with something that heavy. Seems to me that a hawk could kill first, dine on the spot, reduce the mass & fly off with the left overs if it wanted, though! Anyway, after that experience (RIP, Ruby!) we penned the hens for good. I will occasionally turn them loose the last hour of the day, just so they don't go insane. We have a huge, huge coop (25'x 15') & plan to add a run this spring, but after having the run of the property, 25'x15' still must seem like a prison. I keep replaying the movie "Chicken Run" in my head, lol. So I take an occasional chance & hope the odds of surviving their weekly free hour are stacked in their favor.
Let us know what happens! Good luck!