In the U.S., most people would have no idea that a man is wearing a certain head covering to show that he is mourning. This isn’t part of our American culture, and it would be confusing to others and might cause talk and speculation.
It would be sad if someone, not knowing the meaning of the head covering, made a light-hearted comment to the man about his head covering–this might make both feel bad.
A head covering might also draw attention to the man; I would definitely be distracted by a man wearing a head covering during a Mass, since this is still considered bad manners in the U.S. (although admittedly, many young men wear baseball caps and hoodies to Mass and don’t bother to take them off even during the pastoral prayers).
IF the man is from another country, and almost everyone in the parish knows that the man is from another country, then it would be appropriate for him to wear whatever head covering is worn in his country to indicate mourning because people would understand the meaning of his action…
I agree that a black armband is appropriate, somber, and is understandable to most Americans.
I’m sorry for whatever has happened to cause the man in question to be in mourning. I hope that he finds comfort and peace.