1. Rule 1 is don't ever repair a rental and, if you do, only do so with the rental company's express written authorization.
2. I have not seen your Hertz contract(s), but if they were standard Hertz contracts, you did authorize Hertz to post the debits for the damage and the time the car was out of service to the CC you provided.
3. You can trye the chargeback, but Hertz is very good about documenting these things and will simply supply your CC issuer with the damage information and the contract provision. Rarely, if ever, does Hertz lose these.
You are far better off working with Hertz on this than attempting a chargeback. You may reach a deal with Hertz. With the chargeback, once you lose, you owe.