This sign is more than a jovial handshake. Its older, formal gesture was a hands-to-shoulders embrace and a kiss on both cheeks (still seen in many cultures), but this might be too much to restore.
The deacon and priest “model” the gesture for everyone. They also show by their example that this is a ritual gesture requiring simplicity and decorum, not a frantic attempt to shake hands with everyone in church.
The words exchanged might simply be, “The peace of Christ.” This is never a time for hellos or chitchat. This is an act of liturgy.