When Peter looked at Jazz and was trying to figure out what to do with him, he had a rare light bulb moment for himself. He had his soul weapon with him. It was an item type that allowed him to change a users appearance however he wished.
The thing was, the item didn't have to be used on just allies and friends for disguises, they could use it on Jazz. When rescuing Vorden, the plan was to replace him with Jazz while wearing the disguise.
If anyone came to visit him, it would look exactly like Vorden had never left. Even if he shouted and told people what really happened, they wouldn't believe him. After all Vorden was a prisoner, and it made sense for him to try and say whatever he wanted to get let out.
