Why?
In the Bible, there aren't any verses describing Jesus' hair.
There are verses that describe how Jewish men were to take care of their hair according to biblical Law.
Based on these verses, it is likely that Jesus had neatly trimmed black hair, long sideburns, and a beard.
(Both images that you use for reference have an image with long hair.)
50 years after Jesus' birth, in A.D. 57, the Apostle Paul wrote to believers in Corinth explaining that it was a disgrace for a man to have long hair.
"Does not nature itself teach you that if a man wears long hair it is a disgrace for him, but if a woman has long hair, it is her glory? For her hair is given to her for a covering." (1 Corinthians 11:14-15)
Jesus was faithful to follow the Law given to Moses.
He explained to his followers, "Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them" (Matthew 5:17).
Nope, no one and no "image" or painting has a true rendering of our savior and that includes the Turin shroud.
I would think that this image would be closer to the truth:
Of course, like everyone else I have no proof.
I can only go on the scriptures.😟