Pred, there's nothing wrong with doing a FTF (private sale) in Kentucky.
It's perfectly legal.
However, you should look at his DL and write the info down. You don't want to be the last known owner in case the guy flips-out & decides to do... whatever with the thing.
Trading information protects both of you so expect the buyer to do the same (for all he knows the firearm could be stolen). If everything's cool, nobody but the buyer & seller will ever see it.
I'd suggest printing out two copies of a bill of sale with both of your addresses, DL #s, the serial number of the gun, the exact date & time, and both of your signatures.