Indigenous cavalry units in British India were split among three "Presidency armies" and the more central India Army, which absorbed the other forces in 1895, and then all of them were subsumed by Lord Kitchener in his reforms into the Army of India from 1903-1947; cavalry brigades were typically formed of one British and two Indian regiments. While the British were issued weapons and gear, the Indian regiments used the silladar system for recruitment, where they would buy their horse and equipment, and would be cashed out on retirement.

Which is to say, there was room for variation in cavalry swords in India during this period. Most of the troopers in British cavalry regiments in the early 1900s would be using the 1887 pattern cavalry trooper sword, although it was possible to see some older models mixed in there, as well as conversions (a new blade on an old hilt, etc.), and officers (who bought their own weapons) could have off-pattern swords. In 1908 the British adopted a new pattern of cavalry sword with a heavy dish guard and a straight blade, which would be issued to troopers and phasing out the older models; in 1912 the pattern was adopted for officers.

Several patterns of sword, including the 1887 and the 1908 were created in variant patterns explicitly for service in India. A 1910 variant which combined a heavy tulwar-style blade on a three-bar hilt was created, but due to the outbreak of the Great War in 1914 was never put into production; the Indian P1908 instead became the standard weapon.

It should also be mentioned that British cutleries became major manufacturers of blades, which were in turn exported to India and fitted onto hilts by Indian blacksmiths, resulting in a large number of tulwars, sabers, and other weapons whose blades were made and proofed in Britain. These were not, as I understand, exactly issued to Indian cavalry units, but purchased by the members as part of their entry into the unit, and unit preferences as far as style and length could vary considerably.

My general reference for such works is The British Cavalry Sword From 1600 by Charles Martyn, but there's a lot more to Indian cavalry swords of the period than what's in that sole book. You might also look at the folks for r/swords who might have better sources than I do.