Nowadays, following the fashion and western culture is at its peak. Especially, those who live in mixed cultures are very much affected by this. That’s why mixing of men and woman, eating at the same table, shaking hands with each other and contacting each other is not considered wrong at all. Instead, those who consider this as a sin are termed uneducated and with old fashioned.
When looking at a non-Mahram itself is a major sin, then imagine how worse is a sin is to touch her and shake hands with her, as by touching there is a great danger of corruption.
Touching non-Mahram women is such a grave sin that the punishment given to the one who does it is much more harsh than the agony felt on the head being pricked by an iron needle. As given in the Hadith:
Translation of Hadith: It has been narrated on the authority of Hadhrat Ma’qil bin Yassaar (May Allah Ta'ala be well pleased with him) that the Holy Prophet (Sallallahu alaihi wa sallam) said: It is better that your head be pricked with an iron needle than that anyone from among you touch a non-Mahram woman. (Mo'jam Kabeer, Hadith No. 16880; Kanz Ul Ummal, Hadith No. 13065)
When non-Mahram man and woman meet in seclusion, then the third one among them is Satan who encourages them to sin and presents the sin in a beautiful form. It is narrated on the authority of Hadhrat Abu Umama (May Allah be well pleased with him):
Translation of Hadith: The Holy Prophet (Sallallahu alaihi wa sallam) said: You avoid being alone with women. By Him who holds my life in His hand, no man is alone with a non-Mahram woman but that Satan comes between them.