This is going to sound awful, but it is an easier way to cull, if you don't want to see anything.....
Put the chick in a brown paper bag, and gently close the bag. Go outside, and place the bag on the sidewalk. Drop a very heavy brick or large rock on the bag. It will die instantly, and never know what happened. It will be over immediately, and then you can bury the whole bag if you want. You won't have to look at the little chick.
This way, in my opinion, is the easiest way. It all happens so fast, that I want to think the baby doesn't really feel anything. It is dead in a split second, and bonus--you don't have to look at it. This is never easy, no matter how many times you have to cull. Each chick is a little precious life, and when one is suffering, it deserves to die as quickly and humanely as possible.