All perfect praise be to Allah the Lord of The Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Scholars of the four Islamic schools are agreed that it is forbidden for a woman to shake hands with non-Mahram men. This is attested to in the Hadith reported by Ma`kil Ibn Yasar that the Messenger of Allah said: "It is better for a man to be stabbed in the head than touch a non-Mahram woman." {Transmitted by Tabarani in Al-Mo`jam Al-Kabir, Vol.20:p.211}. Ibn Hajar said that its Isnad (Chain of transmitters) is authentic and the same was said by Al-Montheri and Al-Haithami. He (PBUH) used to say: "I don`t shake hands with unrelated women." {Transmitted by Nasa`ei, No.(4181)}.
An non-Mahram man is every man who is lawful for a woman to marry, even after the hindrance is removed. This includes men temporarily forbidden in marriage, such as sister`s husband and maternal and paternal aunt`s husband; all of whom are forbidden to shake hands with.
Nullification of wudu` in the event a woman touched her husband or a noon-Mahram man is one of the famous controversial issues amongst the scholars of the considerable Madhabs (Schools of Islamic Thought). Some narrations that are incompatible in their apparent meaning were mentioned and the scholars of each school held on to their interpretation of the evidence from the Quran and the Sunnah and all of them are Mujtahid (a jurist who performs independent reasoning in finding a solution to a legal question) and rewarded for that.
As for the scholars of our Madhab (Shafie), they stated that when a man touches the skin of his wife or any non-Mahram woman, even without desire, it invalidates wudu`. They have based this view on the verse in which Allah says {What means}: "If ye are in a state of ceremonial impurity, bathe your whole body. But if ye are ill, or on a journey, or one of you cometh from offices of nature, or ye have been in contact with women, and ye find no water, then take for yourselves clean sand or earth, and rub therewith your faces and hands" {Al-Mai`dah, 6}.
Imam Al-Shafie (May Allah have mercy on him) interpreted " ye have been in contact with women" as when the skin is in contact with the skin, even without sexual intercourse. However, the Hanafi scholars said that touching woman can never invalidate wudu`, whether she is a wife, a non-Mahram or a Mahram woman, with or without desire.
Maliki and Hanbali scholars have combined the evidences of the above schools where they said that the touching that nullifies wudu` is when the skin meets with desire and this is the intended meaning of the above verse. As for the touching that happens without desire, as stated Aisha in the two narrations mentioned above, it doesn`t invalidate wudu`.
The fact that other schools of thought stated that a woman touching a non-Mahram man doesn`t invalidate wudu` can`t be used as an excuse for touching and shaking hands with the opposite sex under the pretext that it is something normal. And Allah the Almighty knows best.