I'd just be worried that they'd move as I pulled the trigger.....You really had me thinking back. For the few chickens I've had to dispatch, I've nursed them along until there was absolutely no hope. They were at the point of sitting in one spot quietly.
However, in case you're meaning putting chickens down for slaughter, I don't shoot those. I'll be using a hatchet and a block. Very different
...why I use broomstick CD for euthanization and cone/throat slit for slaughter.