Language: Persian ?
Source: Period account
Hakim shahi is the name of a specific kind of Indian hilt, commonly used for the talwar sword.
Hakim shahi hilts have a pronounced V shape where the grip merges into the crossbar:
Two talwar hilts illustrated in Hendley's Damascening on steel or iron as practiced in India. 1892.1
Left: Hakim khāni
Right: Hakim shahi
It is never explicitly mentioned in the literature, but going by the illustrations in Hendley's work we can gather that the the general rule is as follows:
Hakim khāni hilts have a smooth transition between grip section and crossbar.
Hakim shahi hilts have a pronounced V shape where the grip merges into the crossbar.
Other hilt types
In addition, Hendley makes mention of a karan shahi hilt.
Karan shahi hilt as illustrated in Hendley's Damascening on steel or iron as practiced in India. 1892.
The karan shahi style is quite distinct with pointed grip section and wide quillons. As a type it is associated primarily with the Marwar region in general and Jodhpur in particular.
Hermann Goetz, writing in 1950, sheds some light on the origin of the term:
"The costly damascened swords in pure Mughal taste (figs. 67, 68), were first introduced by Karan Singhjī and, therefore, were termed "Karan Shāhī".
1. Thomas Holbein Hendley; Damascening on steel or iron as practiced in India. W. Griggs & Sons, Ltd. London 1892.
2. Hermann Goetz; The Art and Architecture of Bikaner State. Bruno Cassirer, Oxford. 1950. Page 124 - 125