Praise be to Allaah.
Neither of the two customs which you mention have any basis in Islamic texts. We should follow the Sunnah and keep away from innovations in religion. The best guidance is the guidance of Muhammad (Peace & Blessings of Allaah be upon Him); the most evil of things are those which are innovated; every innovation is a bidah and every bidah is a going astray.
Know, may Allaah help me and you, that the reservation concerning this matter does not have to do with shaking hands with a Muslim brother or raising the hands in duaa to Allaah; it has to do with the timing of these two actions, following the prayer, and making them a regular habit. If one were to raise ones hands between the adhaan and the iqaamah, as is encouraged in the Sunnah, or shake hands when meeting ones brothers on the way into or out of the mosque, or when seeing a brother next to one after a long absence, there is nothing wrong with that at all. We ask Allaah to help us to follow the Sunnah and to follow in the footsteps of His beloved, Muhammad (Peace & Blessings of Allaah be upon Him).
And Allaah knows best.