12C clear.
It was only a tiny slice of time, it was enough for the axe to swing its  errant path. The hit only took a thin slice from my thumb. Lucky it wasn’t worse, or unlucky to happen in the first place. That makes me luck-neutral.
A cut from a sharp edge is usually less painful, and less prone to infection. My only grumble is the site of the injury- it’s on the side of my the joint just where I normally apply pressure when changing gear on the commuting bike.
Perhaps change gear like a good fixed-gear rider.