"Sin" and "trespass" are legal terms that refer to violations of the Law.
Paul, being trained as a Pharisee, was precise in his language especially as it referred to matters of the law, sin, and trespass.
"Disgrace" - ἀτιμία- is best translated as "shame" and is neither sin nor trespass, which would be translated as παράπτωμα.
Nor is there anything about head coverings (excluding Nazaretes and various treatments for Leprosy) in the Mosaic Law, and it would be a repudiation of everything Paul taught to argue that he was trying to impose a Law of Haircuts on the Corinthians after repudiating circumcision and adherence to the Law of Moses.
Rather, Paul was here talking about matters of church order. He did not want the wife to shame the husband, or the husband to shame the wife, or the rich to shame the poor, and so he admonished the Corinthians, having a discussion about what is proper behavior,
by urging them to dress modestly, for those who are wealthy to not adorn themselves extravagently when meeting in fellowship with believers who might be poor, for wives to not embarrass their husbands by flaunting their hair, etc.
It seemed that the church in Corinth experienced a revival of freedom in response to Paul's message of freedom, and they started flaunting local customs when they met, which was giving them a reputation in the city for looseness and was also causing some of the men to feel shamed as their wives exposed themselves in a manner that was looked down upon by the local community:
It cannot be unequivocally asserted but the preponderance of evidence
points toward the public head covering of women as a universal custom
in the first century in both Jewish culture ([apocryphal] 3 Maccabees
4:6; Mishnah, Ketuboth 7. 6; Babylonian Talmud, Ketuboth 72a-b) and
Greco-Roman culture (Plutarch Moralia 3. 232c; 4. 267b; Apuleius The
Golden Ass 11. 10). The nature of the covering varied considerably
(Ovid The Art of Love 3:135–65), but it was commonly a portion of the
outer garment drawn up over the head like a hood. It seems that the
Corinthian slogan, “everything is permissible,” had been applied to
meetings of the church as well, and the Corinthian women had expressed
that principle by throwing off their distinguishing dress. More
importantly they seem to have rejected the concept of subordination
within the church (and perhaps in society) and with it any cultural
symbol (e.g., a head-covering) which might have been attached to it.
According to Paul, for a woman to throw off the covering was an act
not of liberation but of degradation. She might as well shave her
head, a sign of disgrace (Aristophanes Thesmophoriazysae 837). In
doing so, she dishonors herself and her spiritual head, the man.
Paul was trying to reign these tendencies in, hopefully in a discussion with adults in which no one needs to cry out about this or that being a "sin" as they demand a new Law.
All things are lawful for me, but all things are not expedient: all
things are lawful for me, but all things edify not. 1 Cor 10.23 KJV
David K. Lowery, “1 Corinthians,” in The Bible Knowledge Commentary: An Exposition of the Scriptures, ed. J. F. Walvoord and R. B. Zuck, vol. 2 (Wheaton, IL: Victor Books, 1985), 529.