[Graves]

"You are missing the point. When the priest says 'Let us offer each other a sign of peace' what do you do?"

It's not an issue for me as I do not attend religious services with Roman Catholics. In the Orthodox Church, the exchange of peace is normally exchanged at the altar during the Proskomide as follows:
"Priest:
I love You, Lord, my strength. The Lord is my rock, and my fortress, and my deliverer.

(At this time it is customary for the kiss of peace to be exchanged.)"

But to answer your question more directly, you introduced a false premise, that being that I am at the liturgy for any purpose other than worshipping God. That to me is a very strange idea. Before I became an Orthodox Christian, I used to attend Novus Ordo masses and, quite frankly, I found the exchange of peace in the nave a distraction at best and a possible cause of scandal at worst.

[frogjerk]

CCC 1301 The sign of peace that concludes the rite of the sacrament signifies and demonstrates ecclesial communion with the bishop and with all the faithful.116

116 Cf. St. Hippolytus, Trad. Ap. 21:SCh 11,80-95.

[frogjerk]

Before I became an Orthodox Christian, I used to attend Novus Ordo masses and, quite frankly, I found the exchange of peace in the nave a distraction at best and a possible cause of scandal at worst.

That's very odd because I have not experienced anything like that. The Sign of Peace at my Parish's Mass is never anything like that. It is a very cordial, but brief, acknowledgement of who your neighbor is (according to local customs a handshake).

[frogjerk]

I'm sorry I assumed you were Roman Catholic because you were on this thread commenting on the reforms.