The “Sign of Peace” is often one of the most aggravating points of a Roman Pauline Mass. The ancient practice has been taken so far out of context that it amounts to a bunch “howdy do” handshaking that entirely interrupts the sacred Mysteries taking place. Fortunately, I can avoid them at the sparsely populated weekday Masses I attend as the faithful there have the good sense not to walk several pews over to shake my hand.
If anyone wishes to see this practice done right, done reverently, and done in the manner the early Christians would have done it, then watch from about 46:45-50:00 in this video. Feel free to watch more if you are interested in the fascinating Armenian Rite (which has very pronounced elements of the Byzantine, West Syrian, and Roman Rites).