Which side to swing from
The question of whether you swing the prop from left or right or from front or behind must, I assume, depend on the direction of rotation of the engine.
In the days when I flew hand swung aeroplanes, the engines in use were mostly the Blackburn Cirrus Minor and the de Havilland Gypsy Major. These engines rotated anti-clockwise (seen from the pilot's seat) and so were ideal from a hand swinging point of view because a right handed hand prop swinger could stand ahead of the descending blade and swing with his/her right hand.
I have never been trained to swing an American engine, but what I do know is that hand swung Lycomings rotate clockwise. So presumably a right handed prop swinger would only be able to swing them from behind the descending blade while standing just in front of the leading edge of the right wing. I have seen this done, but to me it looked very hairy. I certainly wouldn't like to try it myself.
Broomstick.