How can I avoid shaking hands without having to always explain the terrible arthritis in some of my fingers?

Wave. Give a quick wave and say, " hi, nice to meet (see) you. I have arthritis and my doctor wants me to avoid shaking hands." repeat, "it's nice to meet (see) you.".
Arthritis. Senator bob dole used to carry a pen in his hand to avoid shaking as a result of war injuries.