Sorry, but that is not correct. The modern concept of the image of Christ actually started about the 5th Century with the Christ Pantocrater, a mosaic found in Turkey. The study of iconography has a lot to say on the appearance of Christ throughtout the ages... Durer was latecomer.
Portrait of Myself at Age 28
Albrecht Durer (1498)
The shroud was quite well known by the time of Durer's career and many painters were already using it as the source of the inspiration for the appearance of Christ. Durer shows some knowledge of the Shroud as a single piece of cloth in his painting the Lamentation for Christ. Joseph of Aramathea is portraid holding onto the foot of the Shroud and the top of the Shroud is draped across Jesus' loins for modesty. In addition, his knowledge of the Shroud is also shown by Mary placing her finger in the wound IN THE WRIST, which was contrary to contemporary iconography. Durer was, however, a stickler for detail and he noticed this. Note also the supine Christ has the wisp like structures on his forehead.
Lamentation for Christ
Albrecht Durer (1503)
I searched the Internet and Durer biographies and nowhere did I find an attribution to Durer of the modern appearance of Christ's image. In fact, Durer himself only admitted to ONE deliberate usage of his own face is in a portrait he cakked "Christ the Man of Sorrows".
Christ as the Man of Sorrows
Albrecht Durer
This painting is hardly our modern idea of the appearance of Jesus Christ.