Noah Rocco might be stupid at conjuring answers out of thin air, but he was quite good at piecing things together. The Satan in front of them was a copy, and Noah confirmed that the longer he stayed enveloped by the demon prince's oppressive presence. Since this was a copy, then its 'conscience' would be easier to disrupt.
Noah managed to destroy Nadin Jaeger's body by shrouding him in darkness, devoid of the wrath witch's sight and conscience of what he should look like. Since his mind was in shambles by then, it was easy to manipulate him in thinking and taking over the form his body was taking.
