Most persons who are familiar with the use of the axe would not attempt to swing one one handed. If you don't have an axe try swinging at a _base_ball or golfball one handed and see how effective you are. Ever seen a game of Polo? The p_layer_s are mounted and, using only their right hand, swing a wooden mallet to make contact with a ball on the ground, while other p_layer_s from the opposing team attempt to do the same thing. It is not a big ball, probably about the size of a _base_ball, maybe even smaller, the head of the mallet is of a similar diameter. With practice one handed swinging can be pretty accurate. Rounders, a game similar to _base_ball, also uses one handed swinging. But not the horses. Shame, really.

Come to think of it, I used to use an axe to split kindling wood, and I used it in one hand. Not a war-axe, I hasten to add...