[The Might]

there could also be possible that he did think of Cirith Ungol himself, but only if he was there to help the Hobbits, and not if they would have been left alone with Gollum to lead them...still, considering their way on the Morgai Road there doesn't seem to be any other Orc keep in the mountains between Cirith Ungol and Durthang. There might have been small valleys made by small rivers in the mountains, as we see in the book when Sam and Frodo find a small spring after entering Mordor...so the theoretically it might have been possible.