According to Rabbi Moishe Dovid Lebovits in his recent sefer Halachically Speaking 3 (YWN has many excerpts on this site of the earlier parts of the series), Rav Belsky was very stringently opposed to shaking a woman’s hand.
He also cites poskim who forbid accepting (or giving) change directly from a woman (i.e. a cashier) since there is a concern of touching, and say the change should rather be placed on the table.