You know, I went through this last year.
I had settled on my husband doing the slaughtering, because the thought of the cut went right through me. Go figure he was on a 48 hour shift when one of the meat roosters legs went out.
I fashioned a quick killing cone, and stood there with the rooster sat under it. Put my headphones in and probably did 6 frantic walking loops around the house.
IT. IS. HARD. It is not supposed to be easy. It is very difficult for about 30 seconds, then it gets easier and more mechanical. Dispatching is not a breeze though. Try headphones with music on (though I'll never hear Summertime Sadness the same way again). I didn't want to hear anything, so that helped. Find where you want to make the cut, and don't hesitate. Don't expect to get it right the first time, I had to readjust my cut the first time because I wasn't pressing hard enough.
You will be fine.