I have just ordered a copy of-
Warfare in the Sokoto Caliphate: Historical and Sociological Perspectives. Cambridge university.
-from an inspiring extract I was able to glean that in the 19th century the adoption of cavalry was a revolutionary tactic. From that one might assume that the short form is the more original version? Like the picture of the Dha an infantry weapon. Until I have the book I will suggest that the French blade may well be a late adoption.
The extract at the bottom of this link might also throw some light on the short version.
http://www.jstor.org/pss/182766