For what it is worth, if you are upset about the possibility of accidentally pulling the head right off (which is not a problem for the *chicken*, but having done it myself I would agree it is a bit offputting if you did not realize it was going to happen) you actually might be better off doing the job by hand rather than using a broomstick.
Reason being, 7 wk old "normal" chickens (i.e. not CornishX broilers) really have quite weak and flimsy necks. With a broomstick you will not have the same ability to feel exactly what's going on as it occurs and could more easily overdo it; whereas with the chicken in one hand and the head in your other hand, pulling down and back "like opening an old-style pop can" as silkiechicken once very helpfully described it to me, it is easier to feel the moment that the spine disconnects, and stop *then*.
As far as dealing with it emotionally, I think we are *supposed* to find it rather sad and upsetting to end another living creature's life, but this is for the best possible reason. Remember that it is GOOD of you to be overcoming your aesthetic reluctance to do what's best for the chicken's sake.
Hang in there,
Pat