The possibilities seem endless, depending on who you believe.
Kay Kendall. My problem with her is that she seems to have a very well documented past and a large, extended family in Britain. And if Kay was Timmy/Shimmy, was Rex Harrison his lover or just helping out with the charade? And why choose to have Kay die such a painful death? How did they fake the grave? And nobody blabbed before now?
Josephine Hull. Loved her in Arsenic and Old Lace and Harvey. Sure, I guess she could have been a man in drag, but she was an elderly woman. Many elderly women on film looked mannish back then. The problem with Josephine is her body of work prior to Hollywood - - excessively extensive. The blind item on Timmy/Shimmy didn't mention 50 years on the stage prior to film work. Unlikely and seems a longshot.
Marie Dressler. One of the most underrated actresses of the 1930s, she could (and did) steal a picture right out from under the likes of Greta Garbo, Jean Harlow, John Barrymore and Wallace Beery. While she was rumored to be batting for the same team and never married, Marie is about as unlikely as Josephine Hull. She has an extensive stage background, was a huge vaudeville star and she could hardly fit the description of Timmy as a slight man.
Anne Revere. Presents major problems, mainly because she continued acting on television dramas into the 1970s. That alone should cancel her out, but because of the awards and her unusual looks, her name keeps cropping up here and there.