[BlueDragon]

I too have pondered upon the sort of things you speak of, in relation to the Turin shroud, but this portion;

Since the Bible says long hair is shameful for a man we can conclude our Lord had short hair.

neglects that Jesus was a Nazarene.

If he were to have taken a vow of a Nazerite, included within the vow was prohibition to cutting the hair of one's head, or corners of the beard.

Samson was such a one or similar, it is understood.

[ConservativeMan55]

bttt

[bogusname]

To be a native or inhabitant of Nazareth is all it takes to make one a Nazarene.
However to be a Nazarite is something different altogether. When someone makes the vow of the Nazarite they then must abide by those conditions all of their days. This has nothing to do with being from Nazareth as Christ was. Christ did not make the vow of the Nazarite. A Nazarite can not drink anything that comes from a grape. Christ drank wine. A Nazarite can not touch a dead body. Christ took the little dead girl’s hand and told her to get up. A Nazarite can not cut his hair. Christ had short hair.
You are getting the two terms confused like many folks do because Nazarite sounds like Nazareth. One is a vow and the other is a place.