Am I obligated to shake hands with my ill-mannered colleague at work who refuses to return greetings, knowing that he does not speak to others at work?

Boycotting (hajr) is of two types: The first is boycotting for the sake of one's own ego or for a worldly matter. This is forbidden and not permissible for more than three nights. The second is boycotting for the sake of Allah, due to an innovation (bid'ah) or a sin. This is permissible and has controls and conditions, such as refraining from greeting the sinner and not specifying a duration for the boycott. He may even deserve rebuke until he repents. Boycotting is legislated to discipline the disobedient and deter them. However, if it is not effective or if it increases their transgression, then reconciliation (ta'leef) is more beneficial than boycotting. It depends on the strength and weakness of the one boycotting and the desired benefit.