Many of us butcher our own surplus birds, I highly doubt that anyone is going to get the vapors or pass out from the sight of a little blood. However by not posting you may condemn other of your birds to share the same fate.
Contrary to the fell good nature shows on TV, hawks are extremely poor executioners of chicken sized birds. Not intending to upset anyone but most chickens that are killed by hawks are eaten alive a little at a time. Gaia is a cruel and extremely bloody god never think otherwise.