Help! I broken my hand and fractured my finger and now any handshake comes with pain! How do properly avoid handshakes?

Politely inform the person who is reaching for a handshake about your injury and tell them that, though you are injured, you are charmed to meet them.

Offer them your other hand. Most people will adjust their handshakes, especially if it your hand that goes out first.

I would just tell the person up front about it in a kind and sincere way, I'm pretty sure they would understand