Does it make any difference one way or the other?
The plain teaching of Paul is that man’s head represents Christ.
Christ needs no covering because he did no sin.
Any man who covers his head while praying or prophesying (teaching or giving a sermon or any public talk about scripture) dishonours Christ.
1 Corinthians 11:3 But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God. 4 Every man praying or prophesying, having his head covered, dishonoureth his head.
The teaching is clear.
There are no grounds for a Christian man to cover his head while praying.
I hope you find this helpful.