Unless you have an actual heightened susceptibility to illness (e.g., compromised immune system)—as distinguished from a personal distaste for shaking hands because of a hypothetical possibility of disease transmission—in this culture it is considered to be an insult to another person to refuse to shake hands in greeting, and that is not a message you should be conveying during the sign of peace at Mass. If you do have a documented medical condition that requires you to take higher precautions than most people in avoiding illness, then you should say so by way of explanation. “I’m so sorry, I can’t shake hands; peace be with you” will suffice. Using the word can’t suggests that there is something that prevents you from doing what you otherwise would do if you could.
