Ignore the people talking about "search incident to arrest" (something that ended years ago a la USSC) and "warrantless searches" and other inconsequential minutiae.
If you have to drop something off at the police department then go drop something off. If there is no metal detector to pass through then the topic is irrelevant. If there is a metal detector, tell the person staffing it that you are there simply to drop off paperwork at the desk sergeant and see if they can hold it or do you need to "take it back to my car." If they say they won't hold it, go outside and find some place to hide it on the ground. Under a bush, inside an empty chip bag inside a trashcan, etc.
Your actual task should only take twenty seconds. Your planning for this task shouldn't take hours.