Culling is never easy: it doesn't necessarily mean killing a bird, but removing it from the breeding pen so that whatever fault it has is not perpetrated. Improvement in the standard of your stock is the goal and this includes not only superficial points but utility aspects as well.
There will, however, be the inevitable cockerels that you do not want to keep and only a very, very few will be able to be sold for breeding, so before breeding any birds, this surplus needs to be considered. Should you wish to eat them yourself, that is fine, at least you know how they have lived and what they have been fed on.
On a small scale, the humane way to kill a chicken is by dislocating the neck. There are two sets of blood vessels in the neck and only by dislocating it can you disrupt blood and nerve supply to the brain immediately and therefore first render the bird unconscious and then shortly afterwards, dead. Neck dislocation should only be carried out if immediate unconsciousness is induced without causing pain or suffering. Either get an experienced poultry breeder to show you how to kill a bird humanely, or practise neck dislocation on a dead bird first.
Small numbers of birds on home premises can be killed by neck dislocation without prior stunning which may take two people with a large goose or turkey. (Stunning is usually done in slaughterhouses with one electrode on the overhead line where the birds are hung and the other in a tank of water where the birds' heads are dunked, thereby rendering them unconscious before they are bled.)
It is the responsibility of the keeper to ensure that poultry are killed humanely.
Dispose of carcases legally, check latest regulations on DEFRA website.