No other way ?

[Legate of Amon Lanc]

Yes, I understand, I apologize, but you first spoke about the hobbits and Gollum, so I took it that you are speaking about their situation.
Anyway, you have my meaning of other ways through Ephel Dúath or Ered Lithui - since Cirith Ungol and Cirith Gorgor were the ones most used, and known (and as we can see, in case of Cirith Ungol, not so well known!), I'd suppose that there was not much else to come up with. Personally I wonder if Gandalf had even known what way they should go once they cross Anduin. The only Gandalf's words of this we have near the West gate of Moria:

'We must go down the Silverlode into the secret woods, and so to the Great River, and then -'
He paused.
'Yes, and where then?' asked Merry.
'To the end of the journey – in the end,' said Gandalf. 'We cannot look too far ahead. Let us be glad that the first stage is safely over.

I wouldn't be sure that Gandalf did not know the way to Mordor or did not plan it, nevertheless, he didn't want to talk about it, so we might just guess what plans he had. I don't know if it is safe to assume that Gandalf knew some not-so-well-guarded way through the Mountains of Shadow, even if he had wandered there once or twice, he wouldn't know if the conditions didn't change since that time. We can tell for sure that he didn't want to go through Cirith Ungol - Gandalf seems pretty startled when Faramir mentions it. I also don't know if Gandalf had some plan how to get past Cirith Gorgor, it seems rather suicidal. There will also be the possibility that he somehow thought about coming to Mordor from the northwest or south, but that is, in my opinion, not much of a good idea - this would mean a long journey through barren lands surrounded by the nations enslaved by the Enemy. Which again brings to my mind the question, if Gandalf himself did really have a plan, or if he just thought of "improvising" (for example, if the Fellowship came upon a band of Orcs on Dagorlad and took their clothes to sneak past the guards of Cirith Gorgor). Perhaps he had some preminitions that it would not be his part to choose the way to the Land of Shadow?