I know that if you write the name of a shinigami in a notebook he won't die. But let's say I would write something like this:
John Zeürtö gets scared to death.
At 11:30, John Zeürtö enters a dark alley (name of the alley) with a knife and threatens everyone who is there. Then he sees something not from this world. He attempts to kill the monster, but is unsuccessful. He then sees that the monster is coming closer to him and then he dies at 11:45.
With this, the shinigami would technically kill a human without a death note. And since shinigami die when they kill a human without a death note, this could work. But I also have another example.
Bob Johnson dies of a neck fracture.
At 1:30 pm Bob Johnson enters a mall (name of the mall). At 1:35 he takes cocaine and destroys certain things in the mall. At 1:40 he notices a little piece from a death note in the last regal from a TV store. Then he sees something not from this world and shoots at the monster. After he realizes that the monster is still alive he runs to a staircase to flee. But the monster follows him and pushes him. He falls down the staircase and then he breaks his neck.
Would that work?