Any contract that you sign is binding. Registering you business with the state is not a factor.
Your question does not make it clear if you are looking to make the contract more ironclad or if you are looking for a loophole. However, a contract is a contract. One party is agreeing to pay for the service of the second party.
Laws are different from state to state. Both parties may have to sign the contract in front of a notary to make it legally binding in your state. One hour with a lawyer who deals in business law should be enough time to answer all your questions. I would recommend that you take the time and expense to consult with an attorney. You may need to have a business license in your state and the fines for not having one can be considerable. You might get away with not having one till someone doesn't like the photographs you took at a wedding and sues you. Then all hell can break loose.
Do what you have to do to make your business legal. It works out a lot better in the end.
If you are starting a business, you need to know how to set up your business so that it looks like a business. If you don't, when tax time rolls around, the IRS can declare your business a hobby and require you to pay taxes on your earnings and not allow you to deduct your expenses.
It's worth your while to do things right when starting a small business.
There are lots of books that will tell you everything you need to know.
There is probably a lot of information online as well.
Good luck.
