Does the Hadith: «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» apply to women, and what is the ruling on their shaking hands with men if it does not apply?

The Prophetic Hadeeth: "For one of you to be stabbed in the head with an iron needle is better for him than to touch a woman he is not permitted to touch," indicates the prohibition of a man shaking hands with a non-mahram (definition) woman and vice-versa, and this ruling is not exclusive to men. This generalization is affirmed by the hadeeth: "Every son of Adam will inevitably have his share of zina (unlawful sexual intercourse), for the eye's zina is looking, and the hand's zina is touching..." Thus, a Muslim does not compromise in his religion and does not shake hands with a non-mahram woman under the pretext of avoiding embarrassment. The Messenger of Allah (peace and blessings be upon him) said: "Whoever seeks Allah's pleasure despite people's displeasure, Allah will suffice him against people's burden. And whoever seeks people's pleasure despite Allah's displeasure, Allah will entrust him to people."