For a while, I was confused about the method of Jacques’s death, but now I think I’ve solved the mystery. In TRR, Uncle Monty was killed by having poison injected into his neck, making a mark like a snake bite. In TVV, Jacques was found dead with no marks on his body other than what appeared to be bite marks. Esmé, as Officer Luciana, must have gone into the cell at night and similarly injected poison into Jacques.
While there's no final answer on the manner of Jacques's death, we can at least say that he had no obvious wounds on his body, and Olaf probably did create false toothmarks to incriminate Sunny just in case any of the villagers checked. For that reason, then I agree it's reasonable to think he recycled his strategy with Uncle Monty.