I have read the Shroud of Turin has wine stains and is believed to have been used as the tablecloth at the Last Supper. Apparently there was a custom at the time where the host fed his guests the first bite of food and drink. If true, it would explain the wine stains and provide another historical link against Communion in the hand.
I've never heard, BTW, that the Shroud doubled as a tablecloth. Keep in mind that my own personal leanings are that the Shroud is not authentic, so I tend to be skeptical of the Shroud being used as evidence for anything.