If I got it right, the Black Hand was a name given to a loose confederation of independent gangs most of which used a black hand sign to threaten their victims. Some of its members surely were made in Italy, but I don't think all of them were. For example, Giuseppe Esposito, one of the first New Orleans mafia bosses, wasn't even a mafioso before arriving in the USA, but just a bandit and a kidnapper. Others, like Vito Cascio Ferro, were already made and powerful before leaving Italy.