Is it forbidden for a man to shake hands with a woman who is a stranger to him?

Shaking hands with a non-mahram woman is forbidden, based on the Prophet's (peace be upon him) saying: "For one of you to be stabbed in the head with an iron needle is better for him than to touch a woman who is not lawful for him." This is also due to the potential for fitna (temptation/strife) therein. The Prophet (peace be upon him) himself did not shake hands with non-mahram women, even during the pledge of allegiance; rather, he would accept their pledge verbally. His hand never touched the hand of any woman except one he owned. Therefore, a Muslim should not shake hands with a non-mahram woman, even if he feels embarrassed. He can politely apologize and explain the reason.