If you couldn't get to the jugulars, maybe you were trying to cut in the wrong place. The spots you want are just under the jaw, cut from the earlobe toward the center of the throat. The cuts should be on the sides, so you don't cut the windpipe. Once you've made these cuts, and the bird has bled out, all you need to do to get the head off is cut through the soft tissue the rest of the way around, and twist the head, it'll come off pretty easily. There's a natural weak spot where the neck joins the skull, it pops loose easily when you twist. You shouldn't need anything as strong or heavy as tree pruners. This method also prevents any sharp bone fragments, because you aren't cutting or breaking bone at all. the neck separates at a joint, just the cartilage separates.
