Thanks very much for the long & detailed explanation. I was extremely
suspicious of this rumor, and what you've stated blows it out of the
water.

It's very obvious to me that the screams one hears are those of Fay
Wray herself, especially when one hears her in "Mystery of the Wax
Museum" besides the other films mentioned. In the theater scene, of
course, there are screams of various women in the pandemonium after
Kong escapes, but Fay's voice is totally unmistakable.