Joe,
Those "Italian" lyrics you posted for Little Shoemaker look more like Spanish to me, and when I listen to the Gaylords singing the song, that doesn't appear to be what they're singing either.
Lyr. Req. "Little Shoemaker" (Italian portion)

I'm also trying to find the lyrics to a lullabye The Gaylords sang called "Dormi, Dormi" (not to be confused with the Christmas song "Dormi, Dormi, Bel' Bambin'." No luck so far.