IANAL etc,
There is no requirement for documentation of a firearm sale between individuals within your own state of residence.
The Feds don't require it, the state doesn't require it.
All that is required is that you do not knowingly sell it to someone who does not reside out of state, or who cannot legally own the weapon.
Anything you do in the way of documenting a transaction, or even background checking, would be for your own peace of mind.
Most of the time I just ask to see a Texas drivers license. If they also have a CHL so much the better, end of discussion.
I do make a note of the transaction with the information I have already, usually writing it onto the receipt (if any) from when I bought the gun.
Something like "Bob Sharp, WayCool on TXCHL 972-555-5555, 4/1/08 $425".
I am a little more careful about documenting a sale of a gun on which I have done a 4473, or even if I know the person I bought it from did a 4473.
Most importantly, if you meet someone to exchange a firearm, and you then do not feel comfortable about it for any reason, walk away.