Depicted Pieces of Clothing
There are many, many artworks and movies depicting the crucifixion and in all of them Jesus is wearing a short tunic and a cape that historians think was probably a type of prayer garment rather than a traditional mantle. This was also a garment the one would have expected him to wear to his crucifixion so it likely was.
More Than One
Jesus may have had more than a couple of prayer shawls. The Bible refers to at least on when Jesus removes it to bathe the feet of his devotees and again refers to the shawl being present during prayer with the Messiah.