You thought you'd heard the last of the Fred-Astaire-as-Alfred-E.-Neuman matter but you thought wrong. As several folks have written to tell me, there's a longer clip of the dance number on YouTube — one that includes Fred's introduction to it. In it, he says, "…coming under the heading of things I've always wanted to do, is Duke Ellington's classic composition 'Sophisticated Lady.' Here's our version with Barrie, myself, and the boys." So there's your (almost) final piece of evidence that it was F. Astaire under the mask. You can watch the intro and the whole dance number again here.
And I say "(almost) final" because one of these days, I'm going to be somewhere Barrie Chase is appearing and I'll ask her.