As a footnote, I think that the dynamics evolution of form of both art and weapons follows the same pattern as linguistics, with regards to divergence (from a common influence) over time. In the absence of any formal study on the evolution of the kukri in S. India, these artistic architectural treasures (which predate all but the very earliest illustrated manuscripts - and how many of those from the pre-Mughal South survive to this day?) are probably the best historical depictions and documented chronology we have of contemporary weaponry at the time.
Here's a close-up of both the ayudha katti and the katar in the Shimoga frieze. Maybe I don't have the eyes as you or Jens, but I am unable to discern the detail of the katar from the photo, aside from its general dimensions. What
does surprise me is its rather diminutive size...
Note the fuller shown in the katti above... also the classic Indian treatment of the langlets on the straight-edged sword in the same frieze.