At the time 50 years ago in retrospect it would have been prudent to do exactly that. My mind was not even close to thinking about getting killed. Light was on (otherwise very dark), I came out an overhead door and I wanted to catch the people who had basically terrorized my job site. They were running to the woods and were seconds from escaping, the reason I came out in the first place. I held my hands over my head with the gun dangling from one finger. I identified myself as the caller to them. The cop knew I was not a threat and they caught the active duty sailor and his two nephews who were the criminals. I stood there in that exact same posture until I saw them actually catch the 3 perps. No way I was going to stick it in my pocket, that could have got me killed.
In another incident I was stopped for speeding by a state trooper (grandfather was one in the same state during prohibition). I identified myself as a concealed carry holder, explained to the trooper that I was going to give him my carry weapon, with a single finger while I looked directly at him and did exactly that (wife was in the passengers seat). I then got my wallet, handed it to him and explained that my grandpa was a trooper when there were only 7 in the whole state.
You could see him relax physically with the gun and wallet in his possession and he gave me a warning for what could have been a reckless charge after I explained the circumstances (I was passed on the right then the driver merged in front of me illegally, so I just went around him to get away from an idiot and the trooper saw exactly what he and me had done).
After the warning he followed me for 40 MILES! then passed me and waved goodbye LOL.
This was the same year(first incident) they started selling Subaru's in the USA, my brother called my memory photographic.