The story I heard in a medeival history class about the origin of the handshake is that it's a sign that you don't mean to attack the other person because you're not holding a weapon in your hand

I would guess someone invented the handshake in prehistoric times and we just have no medium in which a record could exist aside from an undiscovered cave drawing or something like that. Humans seem to naturally touch hands outside of any social influence or cultural history. Babies reach out and people touch their hands. It seems like a pretty intuitive human action. We touch things with our hands, so other hands seems natural as a thing to touch. The shake just seems like a minor variation on that.

Chimps shake hands.

https://phys.org/news/2021-05-chimps-handshakes-social-group.html

That is the worst way to describe that.

One silver lining from the pandemic was that fist bumps became more common in lieu of handshakes. Some people's hands can be filthy.