Is it permissible to shake hands with a non-mahram woman, and what is the evidence for that?

Shaking hands with foreign women is one of the widespread reprehensible acts, and a severe warning has been issued for its perpetrator. The Messenger of Allah, peace and blessings be upon him, said: "For one of you to be stabbed with an iron needle is better for him than to touch a woman who is not lawful for him." And Aisha, may Allah be pleased with her, said: "By Allah, the hand of the Messenger of Allah, peace and blessings be upon him, never touched the hand of any woman." Many corruptions result from handshaking, such as arousing desires, weakening jealousy, and the loss of modesty. The actions of some who claim to be knowledgeable do not justify this reprehensible act, and for us, the Messenger of Allah and his Companions are the best example.