Thank you for writing. Personally, I do not see anything being caused by a public handshake between men and women. A good, firm handshake in a public setting probably does not create any wrong feelings. We do this at our church and I have never had any problems to deal with from it. However, perhaps we should go back to the old rules of etiquette. A few decades ago, it was considered impolite for a man to hold out his hand to a woman to shake it. That was considered forward. If the woman did not hold out her hand, he was just to speak to her and not attempt to shake hands. There is no doubt that we have lost our good manners in many things.
But more than the handshake, I find greater problems develop from serious though seemingly innocent conversations between a man and a woman who are not married to each other. We should avoid long or personal conversations in these situations. The emotional link is more dangerous than a simple, physical handshake. I also believe that unrelated men and women need to avoid hugging each other. This is becoming common in many churches and I believe it does lead to problems (not in every case but in creating undue familiarity and opening doors to greater familiarity).