I have no experience of 'sharpies' but in the UK, anything up to pheasant size is most often despatched by a quick spin whilst holding head between index and middle fingers. However, it does take skill and experience to not separate head from bird!
For myself, I nearly always use my thumb stick or a weighted priest, one of which I invariably have with me when shooting, picking up or walking the dogs. I hold the bird by its feet, or both wings folded together over its back, with my left hand, breast facing to my left and sharply hit the back of the skull in a downwards movement. I rarely have to strike more than once, there is some flapping as the bird expires but the head stays attached and there is minimal blood splatter.
This works well for rabbits and hares as well. Rabbits are so delicate that I find a side of a hand applied like a karate chop behind the ears while holding the animal up by its hind legs is usually quite sufficient to break its neck and cause its instant demise.
Geese and ducks are a whole different challenge and I use a humane killer, rather like a pair of pliers.
