I even look to see where the other person's left hand is when they reach out to shake. If I can't see their left hand, I don't shake.
Perhaps you do not realize the Irony of this, but it is great.
Shaking hands developed way back when generaly everyone traveled everywhere armed. Coming into close proximity to other human beings, or a party of human beings out in the sparsely populated world was dangerous and everyone was keenly aware that eachother's co-travelers and themselves were thier only protection. If another group decided to attack them, they would be the only ones coming to thier defense, and there was not a great societal deterant or legal deterant to attack as kingdoms were small and preying on those of other kingdoms was even encouraged (as seen even into America's history with things like 'letters of marque' etc) Many groups entire existance was preying on others, so there was great danger, and everyone knew they were not only thier only defense, but thier own only deterent to attack.
Meeting a stranger and extending your
weapon hand was a sign of great respect as it left you immensly vulnerable.
However that was exactly the point of a handshake, it demonstrated good faith by showing you had no weapon in your weapon hand, and forced you to stick it out there where it could not be ready to react and draw a weapon. A person offering thier weapon hand in such a way was making themself vulnerable to attack as part of thier greeting, which was a sign of trust and good faith because once you had progressed past the point where the opportunity to easily kill the other person was presented, it was demonstrated that was not the intention and trust and a positive relationship could develop. Other things could then be the focus of conversation as immediate personal security was no longer the primary concern.
So a reason for you shaking with your other hand being that you want your
Weapon Hand free is in direct contrast with the reason handshaking ever came to exist.
I just thought I would share as it is quite humorous when you realize the irony.