Regardless of the reason, disposing of a gun is a felony on the right. Nobody whatsoever should ever, ever get rid of a gun. Destroying a gun is a capital felony.
The only minor exception is if you have the handgun registered. Registration of weapons is unfreedomy so the weapon is already tainted and by disposing of it, you are destroying evidence in your guilt in the felony of registering a weapon.
The pro-gun lobby will get Texas to pass a bill that lets you sue somebody if they think you got rid of a gun even if the gun was never used in a felony (minus the exception mentioned above).
Will no one consider the gun's feelings?