You can purchase from a non FFL dealer. What this usually means is the individual has purchased a space and is selling their personal firearms, currently there are no requirements for paperwork on this is type of purchase/sale. Unless OK has changed the law recently there is no requirement to register a gun with the state or local LEO, so there should be no problem with the state.
Just for personal protection, I have always insisted on some form of identification (driver's license), I record the name, license number and state, make, model and serial number of the gun just for my persona records. This way if a situation ever arises where I have to explain where a gun registered to me has gone, then I have the information. If a person does not want to give me the info I tell them to walk.