The original "Fitz" revolvers that were personally associated with J. Henry FitzGerald were all built on steel-framed guns, because "Fitz" was either retired or had passed away by the time the aluminum framed Cobra came along. However a number of gunsmiths who were good, bad and indifferent, continued to modify ordinary revolvers to this configuration, and Colt's service department probably did some for special customers. I know of at least one Cobra that meets the description of the gun in question. It belonged to Paul B. Weston, who was a noted firearms instructor with the New York City Police Department. What I don't know is if it was built by Colt, or someone else.
The Cobra has an aluminum frame that is usually black/blue anodized. If Colt built the one Wkdk2 has it would have been modified before it was anodized. If it was done outside the factory it is possible - even probable - that the metal is bright or otherwise finished where the trigger guard was cut away. Also, because the work was done on a custom basis the workmanship (when it was done at Colt) was impeccable.
Some other points:
Colt usually (but not always) left the single-action feature intact, and checkered the top of the bobbed hammer. Aftermarket guns may or may not be DAO and the top of the hammer is usually serrated or smooth.
The question of getting a factory letter is a difficult one. They are expensive, but if the owner of any Fitz style revolver can prove that their gun originated at the Colt factory the increase in value will more then cover the cost of the letter. The likelihood of a genuine Fitz/Cobra is possible, but not probable.