Yes, one to two weeks looks reasonable, they probably couldn't hold the secret much longer than that anyway.
Iran would release him to the US in a minute. They are playing nice and there is a lot of back channel diplomacy going on. They have a lot to gain by turning him over and nothing to lose, really. You might be right about the Saudi's, if they got him they might not turn him over, but they would end up executing him. At least that way they can save face.
Say we found out he is in a middle east country....how long would it be before we mounted a raid to get him....not very long.
I think it would be a regime's suicide to hide him from us.