Dunno a whole lot about cops and the rules they work under concerning their armament, but I do know that, when I was still AD, if I had ever handed my firearm to a civilian, loaded or unloaded, I would probably have faced, at a minimum, a Field Grade Article 15. More likely I would have faced Summary Courts Martial.
Sorry that the officer is too tender-hearted to do his job; perhaps he needs to be in another line of work. Euthanising a sick, injured, or even dangerous animal is a task that no one with any kind of conscience likes to do, but it is one that occasionally has to be done as in this case.
Handing his service weapon to another person in that situation calls into my mind his ability to make the correct call in a crisis situation.