Imam Ash-Shafa'i and Imam Abu Haneefah, as well as others, are of the opinion that a man must make wudu if he touches (lamastum) any part of a woman. They base their argument upon the Qur'anic aya "...or if you have been in contact with women..." [An-Nisa:43]. They say using one of the rules of Tafseer, that the term lamastum(contact) is defined by Allah in another ayah where He uses the same term to mean simple physical contact "...so that they could touch it with their hands..." [Al-An'am:7]. This opinion is true and absolutely valid except if there is an authentic hadeeth to say otherwise. For all the Salaf-As-Salih have stated that when one comes across an authentic hadith which they were unaware of, and it is contradictory to their ruling, the hadith must be followed and their ruling is to be disregarded.
In an authentic hadith narrated by Aisha She states: "The Prophet used to pray for long hours at night in their apartment, and that she used to sleep in front of him. Because the room was small, when the Prophet used to make sajdah he would tap her calf with his hand and she would retract her legs so he could make sajdah. And when he stood up she would allow her feet to return to their original position. [Bukhari]
Another hadith narrated by Aisha as recorded in the Musnad of Imam Ahmad states that Rasool Allah used to kiss Aisha and then go to pray at the Masjid without remaking wudu. It is clear from this evidence that touching those women whom Allah allows us to have contact with does not break our wudu. As for the term lamastum, Ibn Abas said that when lamastum is used by Allah in the Qur'an reference to males and females that it specifically means sexual intercourse.
As for men and women shaking hands or touching in any other way, this is expressly forbidden. Again hadith narrated by Aisha In describing how Rasool Allah took the oath of fealty from women, Aisha said: "By Allah, Rasool Allah never took any vow from women except that which Allah had ordered him to take, and his palm never touched the palm of a woman. When he had taken their vow, he would tell them he had taken their oath orally."
In another hadith the Prophet strongly warns the Believers about the seriousness of shaking hands with women. It was narrated on Malik bin Yassir that Rasool Allah said that it is better for a Believer to be struck in the head with a hot iron rod than to touch a woman who is not lawful for him.[Tabarani & Baihaqqi]
As in many matters of Deen, some people try to tailor Islam to their own base desires. In this case they use the following accounts as proofs that handshaking with women is not forbidden. In a hadith narrated on Asma bint Yazid it is implied that Rasool Allah used to shake the hands of women when taking the oath of fealty with a handkerchief over his hand. This Hadith is da'if(weak) because of the unreliability of one of the narrators. Another alleged hadith narrated in Ar-Razi's Tafseer states that 'Umarused to shake the women's hands in place of Rasool Allah. This is not only illogical but has been found to be da'if by the scholar Abu Bakr.
Thus, the issue of touching women and making wudu is resolved in a direct and straight forward manner. We must in all of our actions strive to conform to Allah's commands and thereby earn His pleasure. If we are not going to maintain Islamic etiquette and morals, what then will save us from Allah's Wrath? How then do we avoid failure in this life and in the Hereafter? In keeping with this a famous Arabic couplet states, "A look, then a smile, a nod of the head, then talk, a handshake, a promise, then the warmth of a bed."