Very impressing pictures, I was not aware that the Jambaya was that popular still in the modern times. Thank you for sharing them.
Well, I have to admit that I never had a chance to see the horn of a rhino that close and it was always still fixed to the rhino…

But to be serious, the structure of the hilt does not show annual rings and it could be rhino horn. The silver plate with the stones was definitely a part of the sheath fitting, is shows the semi tubular shape, there are small holes at the sides and the size fits perfectly to the dagger blade.
I am not going to clean it perfectly, as I like very much the old patina on the weapon. My other hobby is to collect old Ottoman coins, and a harshly cleaned coin is always worth much less than the same one with the beautiful colour of age. Nevertheless, this does not mean that one should not do essential preservation or sensitive restoration.
My experience with old blades is near to zero, for more modern weapons like bayonets I use only a special oil for guns to avoid rust (a German product called Ballistol) and it is very recommendable. Nevertheless, it only removes thin rust films, not the thick rust.
What would you recommend to do? What is best to remove the rust without damaging the blade? Is there a chemical way or is polishing powder a solution? Or leave it as it is?