My thought is that there is no paradox, "Friday" being the execution day can be a surprise. If the prisoner finds out that Friday is the execution day on Thursday because he is not executed on Thursday, the specific day is still a "surprise," just a day earlier than it happens.
The prisoner is specifically told that the surprise will be such that he doesn't know until the knock on the door on at noon that he will be executed that day.
He cannot be hanged on Friday without that being a lie.
