Should you wear a hat when shooting pigeons over decoys?

A: You are quite right, many is the pigeon that owes its life to having spotted the white face of a shooter peering up at it at roosting time, before a shot could be fired. Were it not for the fact that I do not feel comfortable wearing a veil of any sort, I would use one.
My answer is to lower my face as soon as I spot a bird approaching, not moving until it is directly overhead. Also, I tend to select a spot within the wood which has a bit of background cover, and not worry too much if there is not a big open patch in the canopy above. Provided you ignore the branches and keep your swing moving, enough pellets will get through to do the job, and the pigeon is less likely to see you.