Recently I visited a Fatawa website. In response to a question the mufti stated it is permissible to shake hands with non-Mahrems, if it is done without desire. I have never read anything in the Hadith that state such. Can you please throw light on this matter?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Shaking hands with alien women is an abominable habit that is commonly practiced by many people. The one, who condemns it, is considered evil-minded and suspicious. The Prophet (Sallallahu Alaihi wa Sallam) never practiced it but he severely warn against this practice. M'aqal bin Yasar (Radiya Allahu Anhu) reported from the Prophet (Sallallahu Alaihi wa Sallam) that the Prophet (Sallallahu Alaihi wa Sallam) said: "If one of you were to be stabbed in the head with an iron needle it would be better for him than touching a woman whom he is not permitted to touch" . [Reported by Imam Tabrani and the narrators of this Hadith are reliable, Imam al-Baihaqi also narrated it].      
Ayisha (Radiya Allahu Anha) said: "By Allah, the Prophet (Sallallahu Alaihi wa Sallam) did not take any pledge from women except what is ordered by Allah and the hand of the Prophet (Sallallahu Alaihi wa Sallam) has never touched the hand of a woman" . Moreover, it is known that shaking hand with alien women causes many evils such as arousing lusts, disappearance of bashfulness and losing sense of honor.
Know that if some semi-scholars give a Fatwa that legalizes shaking hands with alien women, this does not change the ruling as stated in the Sunnah and practiced by the Prophet's (Sallallahu Alaihi wa Sallam) companions.
Allah knows best.