Is there a rule for a handshake promise?

Not for the handshake itself. But the promise? That's different. A handshake promise is a tradition that dates back a long way. Let's look at it a bit. Back in the day, men did business with a handshake. It was pretty much universally recognized by all concerned that if you shook on it, it was a done deal. No written contracts, no papers to sign, no fine print. You came to an agreement, you shook (hands) on it, and both parties knew what to expect. From the time they could walk, kids were taught to respect the agreement made on a handshake. Honesty, honor, integrity, personal responsibility. Such uncommon things in this day and age. You didn't shake on anything you didn't intend to follow through on. Your Word was your bond.