I'm not overly concerned with stressing them. Right now I don't have that many (8 different hens;only 3 laying) so I haven't had to touch them to let them out. I don't go out of my way to handle them but I don't give it a thought when I do handle them. I normally try to let them work out all their differences without getting involved.
Right now I have some aggressive ones in the flock. I am introducing a couple of 14 week old pullets (B.O. and B.A.)to them. I had to remove the two most aggressive hens, my beloved RIR and a black sex link. They are the only ones that get blood in their eyes and try to kill. The others just do minor pecking. So I took the two meanies out and put them in the smaller pen I had the pullets in. I'm going to give the pullets up to 2 weeks to get adjusted and accepted by the rest of the flock before the meanies get to come back. Hopefully by then they will be big enough at 16 weeks to not get killed over it.
What's kind of funny to me is that the RIR and BSL are the ones who are acting stressed now. Not because of trapnests, but because they don't have their gigantic pens to run around in anymore. I think tight confinement spaces are more damaging to birds than a whole lot of things. They have plenty of space in the smaller pen,(i used to keep 4 in the same space one time 3x6) but they are so used to the 1000 square foot pen they were in that they go crazy trying to get out when I feed them. I hate to put them in there, but they would kill my pullets if I didn't separate them.
If my chickens get stressed over the few times I handle them when necessary, I will definitely scratch my head. Just being a chicken and living within their feudalistic pecking orders with a big aggressive rooster running around seem to be their primary concerns. I have found that they get used to everything over time.