"Monopoly on violence" means "monopoly on determining who may use violence legally", not "is the only one whose employees may legally use violence."
If the state says, "Alice, you can arrest Bob and bring him in", and Alice is not a sworn police officer, that is not ceding the state's monopoly on violence. (The state would, of course, have liability for whatever their authorized Alice to do.)
If the state says, "Alice, you can arrest Bob and bring him in", and Alice is not a sworn police officer, that is not ceding the state's monopoly on violence. (The state would, of course, have liability for whatever their authorized Alice to do.)