Very problematic.
Thing is, until 1857, the Mughul Emperor served a necessary purpose.
In reality , most of India was ruled and governed by the British East India Company, with the British Government pulling the strings in the background after 1833. But, British 19C law had reservations about the idea of a Corporation possessing sovereign power. Someone obviously had to be the official King, Emperor, Lord High HuffnPuff or whatever. But prior to 1857 to British Government didn't want to take that responsibility officially. So there needed to be a place holder, which was the Moghul Emperor. He was officially the Lord High Huffnpuff, although in reality the Company collected the taxes, and kept or spent them.
But after 1857, the British government declared that the Queen of England was sovereign of India (she didn't actually take the title of Empress until 1870, but sovereignty was vested in the British Crown from 1857, when the EIC was wound up.
Now, you can't have two Lord High Huffnpuffs at the same time (be like having two POTUSs at the same time). So the Moghul Emperor had to go. To keep him, you would need to remove the British declaration of sovereignty. And the Mutiny was only a trigger for that, people had been discussing it seriously for a long time. No Mutiny, the Emperor might have held on a few more years, but no way until 1948
(In actuality , there would have been no problem with the Company holding sovereignty, at least until 1834. Until then, English real property law was based on feudal law, which was very accommodating about such matters. Feudal law didn't really care whether the King was human or not, or singular or multiple.There were plenty of precedents . But the folk of the 18C weren't keen, for various reasons, to wake that sleeping dog up)