It depends on the laws in your state weather or not you can sell a handgun from one private party to another without an FFL. I have sold a few to friends without doing a formal transfer but I always draw up a bill of sale that Ill keep a copy of in my records just in case something pops up down the road.
Some call it the gun show loophole and a few other things. But many states allow the sale with out having to go through a formal transfer. Check with your local LEO. They can give you better info than any of us really. If it was me I'd make sure to at least get a bill of sale signed by you and the person getting the weapon. Just about everyone has a printer and scanner anymore, it makes things a little tidy to have some kind of paperwork that you no longer own the weapon.