"Let us offer...." is an innovation, or at least, after 400+ years of NO kissies, huggies, or whatever, ...now, suddenly, this is important?
A smile will suffice.
Even the most lit-wonk poofter activist in the US, Rembert Weakland, stated that the "sign of peace" is in the wrong place--it should occur at the BEGINNING of the Mass.
But to put a twist on the song: If Rembert's for it, WE can be against it, without fear...
It is not easy to determine the precise link between the "holy kiss" and the liturgical "kiss of peace", known in Greek from an early date as eirene (i.e. pax, or peace). This latter may be quite primitive, for it meets us first in the description of the liturgy given by St. Justin Martyr (Apol., I, 65), who writes: "When we have completed the prayers we salute one another with a kiss [allelous philemati aspazometha pausamenoi ton euchon], whereupon there is brought to the president bread and a cup of wine." This passage clearly shows that in the middle of the second century the usage already obtained — a usage now claimed as distinctive of the liturgies other than Roman — of exchanging the kiss of peace at the beginning of what we call the Offertory.
*My, my...you are wrong about the Last Supper not being a Mass; and you are wrong about the Kiss of Peace; and you are decidely wrong in your hautiness towards others as re a mere handshake.
Is this how you win others to your cause of advancing "traditionalism?"
To me it seems a cause devoid of charity; a cause seriously deficient in knowledge; a cause mortally wounded by arrogance.
Try a little humility, brother. Shake hands with others even if you imagine them unworthty of you.
It will do you good...