Legal agreements, including contingency agreements, are mostly for perception.
If you have completed work, and were not paid, a contract allows you to collect. This part of the contract must be written properly, with teeth.
Write whatever you want in plain English for the rest of the agreement. Contract law, and legal enforcement of such, is intended to determine the intent of the parties who enter into the contract.
That being said, I highly recommend against taking action against someone for any other reason that to collect unpaid bills. Anything else is borderline dishonest, and is grounds for someone to trash your reputation.
Our contract is very simple for anyone to read, because we wrote it with that intent. We did not have a lawyer write it. If your contract is full of legal BS, and statements that people perceive as unfair, they will question your integrity. Why include all that for something you will never utilize anyway.
I would be happy to give you a copy of our contract if you message me.