You ever wonder why we shake hands instead of just say hello ? The origin of the handshake is that it was a way to show that you weren't holding a weapon, at least not in that hand. And I believe the strength of the handshake was to demonstrate that you are strong enough not to be messed with when unarmed. I'm not sure what else you communicate by squeezing too hard. Handshaking is an old custom. So don't stop shaking hands, you just don't need to overpower the other person. It's not like thumb wrestling.