Well, this raises an interesting question--does Zanbizar successfully get some Gulf Arab state(s) to be its patron(s) in this TL?
They'd best get Britain instead to be its patron. Basically a network network with East Africa, the Gulf, and India proper, which is Zanzibar's traditional role brought to the modern era.
If Britain has more of an interest--or for that matter, the United States if it can be framed as "let's stop communism in Africa"--then Tanzania (which would be called Tanganyika TTL since Zanzibar is not officially a part, unless it plays host to a government-in-exile for Zanzibar) can do absolutely nothing against them.
It'll make a decent tax haven, transportation hub, etc., plus there is offshore oil and perhaps tourism opportunities too. It'll be far wealthier than today, though probably not as much so as Singapore, even assuming it gets a Lee Kuan Yew sort of leader. Which Zanzibar absolutely needs once John Okello and the Afro-Shirazi Party coup is defeated. Sideline the Sultan of Zanzibar too while you're at it. Zanzibar would almost certainly be taking in many Indians who were either expelled or otherwise chose to leave from East Africa, at least assuming we have people like Idi Amin in power.
Overall there's a high possibility for Zanzibar to have the highest GDP per capita in Africa and be the most developed nation on the continent, although like Singapore, a high level of inequality is guaranteed.