This I agree with:
First, it would not affect the authenticity of the Shroud, or indeed the truth of Biblical Christianity, if Jesus was crucified on a Y-shaped cross. The Gospels do not describe the shape of Jesus’ cross. But having said that, the evidence is against Jesus’ cross having been Y-shaped.
And this I certainly agree with:
But a medieval forger would have depicted the traditional Roman cross (†) not a non-traditional Y-shaped cross, amongst other things:
"The forger working in France or thereabouts around or before 1350 would have to have been either an overzealous monk whose piety got the better of him or an arrogant swindler who wanted to make a bundle in the underground relic market. Both of these possibilities strike me as unlikely, since the portrayal of Jesus on the shroud is nontraditional, non-European; details like the cap or miter of thorns, the nails through the wrists instead of through the palms, and the nakedness of the loins would not inspire the devotional or artistic sensibilities of fourteenth-century Europe; rather they would have gotten the forger burned at the stake. Moreover, the accuracy of details like these would not be common knowledge to a potential forger for centuries to come." (Wilcox, R.K., 1977, "Shroud," pp.170-171).