Large numbers of Catholics already weren’t shaking hands before COVID-19. Flu season, arthritis, and cultural differences all cause a lot of people to do something other than shake hands.
Before COVID, I myself generally participated in the Sign of Peace by raising my hand and waving or nodding to others around me. I didn’t shake hands unless someone was very determined to grab my hand and plenty of people were not. The reasons I didn’t included a) a lot of people where I attend church don’t want to shake hands, 2) I am often sitting at a distance from others especially at daily Mass which is not very crowded, and 3) I had several colds or sinus congestions that had me blowing my nose and coughing during Mass and no one wants to be shaking hands with a person who seems like they may have a cold; also there were often people sitting by me doing the same so I didn’t want to shake their hand either.
I have seen other Catholics bow, nod, raise their hand like I do, or give a 60s style peace sign to those around them rather than shake hands.
I have a feeling handshaking as a custom may just die out everywhere and be replaced by elbow bumps or little nods/ bows or something else. I already did my first “elbow bumps” with a new business contact in early March before stuff was even shut down.