Hi Norman,
The regulation British cavalry sabres typically had blades of about 36", though I have seen some officers M1796 sabres quite short. These were I think intended as dress sabres that would not be as obtrusive while being worn at formal events, and not necessarily combat weapons.
In British regulations for the swords for native cavalry, I think there were two prescribed lengths, 31" and 33" for the sabre blades, one for Madras and one for Bengal (I believe this was in one of Wilkinson's books on swords).I would imagine that in sharpening, some of the tip radius would diminish, so the short length could correspond to the shorter length mentioned.
While it is true that the short blade on this tulwar might preclude cavalry use, I think that would be more the case earlier before firearms became primary weapons. The tulwars became more of a secondary weapon that was more likely to be used in melee or dismounted as often the case as action with British forces moved to the Northwest Frontier. I once had the great honor of interviewing a British brigadier who as a young cavalry officer had led one of the last British cavalry charges in the plains of these regions in the 1930's. He showed me an interesting sidearm he had captured from a tribesman which was like a tulwar without pommel disc, and the blade was also relatively short.
Despite lack of markings (weapons in frontier regions were not necessarily monitored in native ordnance with the rigor of British regular regiments) this may well be the early 20th c. piece you're hoping for .
All the best,
Jim