Of course, I didn’t mean literally hand over. Perhaps I should have said, “point to that gun on the ground over there and inform the officer of the gun’s readiness or condition to discharge if were to be handled”.
Have you watched the videos explaining why you should never talk to the police?
Here in Kalifornia we are legally required to register handguns. That means that the gun can be traced to a particular person, assuming it is registered.
I don't know the law in Florida, but Zimmerman might have been well served by saying absolutely nothing. The prosecutors might then be faced with reasonable doubt about whether Martin or Zimmerman brought the gun to the scene. (An empty holster might give the game away, however.)
As it is, Zimmerman has made many statements and anything that he has said that seems to conflict with the physical evidence or testimony from witnesses, however much mistaken, can, will, and is being used against him. Anything he had to say could have been communicated through his lawyer.