I'm not aware of any way to configure a default wrap up code to be assigned after a period of time. You can request new features at https://purecloud.ideas.aha.io/ideas.
The proper thing to do would be to have the agent complete the conversation normally. If that's not an option for some reason, a user with appropriate permissions should use PATCH /api/v2/conversations/calls/{conversationId}/participants/{participantId} to set a wrap up code (if desired) and disconnect the agent participant.
POST /api/v2/conversations/{conversationId}/disconnect is intended to be used primarily for stuck calls, not for normal participant disconnects. "not intended to be the normal way" is a polite way of saying that using that API bypasses normal processes and you may cause undesired data and encounter unexpected side effects by using it.