I really can't think of many ideas that would be worse. You're going to give him a deadly weapon which he has no interest in owning and expect him to be able to use it in the pretty unlikely event that he might someday need to defend himself?
Now, I'm all for open access to firearms for all who might want them for defensive purposes, but no one who does not should ever be forced to own or possess a gun!
Owning a firearm is a tremendous responsibility, and it carries with it a number of risks.
If he is not interested in owning a gun then he will not practice. In fact, he won't even familiarize himself with the weapon. This greatly reduced his chances of using it effectively and greatly increases his chances of MISusing it unsafely.
If he is not interested in owning a gun, then he will not study, learn, practice, and live the four rules!
If he is not interested in owning a gun, then he will not buy a gun safe or take other reasonable precautions about safe storage.
If he is not interested in owning a gun then he will not take the time to learn the local, state, and federal laws about doing so. If he does not understand them and take them seriously, you may have just handed him a ticket to PRISON someday when he makes an uninformed mistake. (In fact, your gift of a handgun may, itself, be a felony violation of your state's laws. Look up your state's laws on transfer of a weapon. If it has to go through an FFL, you can't just give it to him!)
If he's not interested, that's his right. Don't go putting him into a dangerous situation with an unwanted gift of a firearm!
Might as well give him a rattlesnake. The potential risks you could be exposing him to would be less!
-Sam