Is it permissible for a man to shake hands with a non-mahram woman, and what is the ruling on handshaking with a veiled woman who seeks Allah's pleasure?

It is not permissible for a Muslim woman to shake hands with a non-mahram (definition) man, based on the Prophet, peace and blessings be upon him, who said: "For one of you to be stabbed in the head with an iron needle is better for him than that he should touch a woman not permissible for him." This is also because touching is more stimulating than merely looking, and Allah has commanded lowering the gaze. A veiled woman who shakes hands with non-mahram men has done good by her hijab (definition) and evil by her handshake. She should refrain from shaking hands because the Shariah forbids it.