When I was in the RCC, the Sign of Peace consisted of a handshake. I'm not sure how that's a door to licentiousness. The only church in which I've been kissed on the cheek as a greeting, is the Orthodox one I now attend.
There is no definite "sign of peace" in the RCC, so that's just your experience speaking. It can be a handshake, a wave, a kiss on the cheek, or more, sadly. Here's from one RC instruction: "The nature of the sign is to be determined by the culture of the people who express it. In the United States, the bishops let local communities determine the actions and words. We have no set formula or gesture for extending this sign. Most often worshipers will shake hands and say, "Peace be with you." But you may also see them kiss or embrace, wave or flash a two-fingered sign of peace. Although today it would seem cold to omit the sign of peace, it is optional." http://www.rpinet.com/ml/2508bi1.html
Most Orthodox cultures have some level of affection involved in a greeting to begin with, as do many Latin cultures. In such a situation, it would have less import than in a more distant community. That said, in most traditional Orthodox Churches, men are separated from the women anyway, and there is a sense of what is inappropriate. "Doing what works for you" as in the RCC is opening a pandora's box.