No, at St. George we do not do a "sign of peace" during Mass. A few (very few) have asked, "why not?" It is technically allowed in the Divine Worship Mass, but only if the priest decides to do so. I decide not to do so. In the early church there was not a sign of peace, but rather a kiss of peace (it is even referred to multiple times in Scripture!). In different cultures, the "kiss" did not have the same impact; and thus, it was moved to a "sign" of peace (here in these USA that usually means a hand shake--kind of anemic when you think about it).
Yet, in American Catholic churches, the "sign of peace" has become such a loosely monitored, and chaotic moment in the Mass, that I think it should be called a "sign of distraction". There is not much peace when everyone is milling around and turns their attention away from the Blessed Sacrament. I am sure people intend to express peace, but the manner it occurs in most parishes is the very opposite of what can be considered "peace" in the Mass. Furthermore, it feels like the entire Mass is slamming on the brakes, sliding into a ditch, and then is suddenly squealing the tires to get back on the road.
Therefore, I have chosen not to do the sign of peace in our Masses at St. George. Yes, it is still encouraged for clergy at the altar (especially if the Bishop is present) to exchange a sign of peace with one another. On that note, if you have ever seen Bishop Lopes give the sign of peace to his priests, it is not a simple handshake (watch it, and you will see a very traditional thing happening!). Yet, even when that occurs, the laity are still supposed to remain with their attention on what is happening at the altar. They have already had peace expressed to them by the priest, and have extended peace to him in response.
There will come a day when the church can return to a reverent and non-distracting form of the peace. What that will look like, only God knows. In the meantime, we will maintain reverence. We will not have a brief "chit-chat" session in the Mass. We will receive Christ's peace, and rejoice that He allows us to avoid things that can hinder the flow of the Mass. After all, it is not a "worship party", but the eternal sacrifice of Christ our Lord brought into the present time; and we must show proper reverence in all of that glorious event.