First, anyone who is sick is excused from the obligation to attend mass. I think it's true to say that many people never much liked the Sign of Peace to begin with...the modification we are discussing has NOTHING to do with eliminating it, simply not making it a source of germs.
In lieu of a handshake, a polite bow, a wave, a smile, a gesture of blessing all might be suitable. We should be understanding if someone chooses this as an alternative to the handshake.
Anyone who travels in Asia knows how important a bow is for the Japanese. Here's an interesting clip from a travel article. The Roman Ritual prescribes a simple bow of the head (before communion, for example) and a profound bow of the body (to the altar, for example). These would be roughly equivalent to the first and last bow in the accompanying diagram. A simple bow of the head to each other at the Sign of Peace would surely be suitable.
Let us pray for health and safety during this season, and do whatever we can to help God keep us that way.