The handshake was a good move. Shows confidence, poise, some form of adherence to 'civility', and tradition. it's a nod to old school politics. It's also a gesture of strength. sometimes you are shaking someone's hand in a social setting to tell them don't fukk with me. Esp. among men, you give or get that real professional formal shake, you are sending a message.
If there HAD to be a second debate, and I think she should just brush him off, and let him cry about it, she should completely pivot and be entirely civil and just talk about American people and all that shyt.