Salaams Ibrahiim,
For my own (and possibly others') clarity, when you discuss "wing-shaped" swords or blades, are you speaking of a blade with a lenticular cross section, i.e., a double-edged, "flattened" oval?
Also, can you please elucidate in detail the blade profile of the Omani swords you believe to be of indigenous form and which you describe as being "flat" by comparison (with regards to presence of lack of distal taper, thickness, etc.)?
As a "math guy," I guess I am surprised I don't see more quantitative analysis of measurable parameters in the study of arms & armor, such as blade length, width, profile, as well as easily measures yes/no parameters (e.g., taper, distal taper, etc.). In fact, the only time I can recall seeing tables of data was in regards to a New Zealand study of Polynesian (or maybe pan-Oceanic) war clubs (I'm guessing there are probably more out there, but just not in my nascent library). It's the least subjective of expression of form, and I would think a proper statistical analysis of the respective blade forms would be the least interpretive way to test - or support - your theory.
Cheers,
Chris