It's unlawful. The proof for the judgment that a man’s handshake with a marriageable female (ajnabiyyah) from her age of desirability, is Islamically unlawful is the Hadith of The Prophet, salallallahu ^alayhi wa sallam, he said, “If Allah  willed to punish the man who sinfully  touches a marriageable woman, his punishment would be more severe than to be stricken on his head with an iron bar. ” (Related by Al-Daraqutniyy.

The Prophet also said in another hadith related by al-Bukhariyy, “The adultery of the hands is the forbidden touch (zinal-yadan).”