I feel like expanded rule through princely states rather than direct rule by the Raj could create a situation where when the British leave, not much changes on the ground. Same princes, same countries, same government; there's just no top layer of British rule over the princely bureaucracies.
While war might eventually occur in such a situation, I don't think it would be an immediate result as long as each princely state was large enough and strong enough to stand on its own.7