Andaman and Nicobar Islands? No (Wikipedia tells me they are in the Bay of Bengal).

Interestingly, Wikipedia shows the Indian Ocean going as far as the Malay peninsula and therefore including my guess. However that does also mean that several hundred Indonesian islands are also possibles.

Sentosa? No.
My reading of wikipedia is, roughly speaking, that there is one pretty broad definition of ocean, whereby pretty much all salt water is included in one ocean or another. Within these oceans there are then various pieces of water that have their own names -- example, the Bay of Bengal is part of the Indian Ocean. But there is also a narrower definition, in which the oceans are basically all the unnamed left over bits.

Excuse me for having 2 goes in a row - but at least it's not a guess at the answer.
That was my understanding as well, but I hadn't really thought about the implications in that part of the world, if you're going to say that you go directly from the Indian to the Pacific ocean.

East Indian? No.

Australian? No.
Komodo? No.
Not sure why it is proving so hard to narrow this down, other than the fact that people are doing a fair amount of guessing of places that have already been ruled out, and people are jumping perhaps too soon to guessing particular places.

What you know: This is an inhabited non-volcanic tropical island, one of a group, smaller than the Isle of Arran, not recently in the news. Rock climbing occurs there, and it does not have significant amounts of water on it.

It is located in a named body of water that is typically understood to be in the Indian Ocean. (As long as we are taking the broad definition of ocean there is no ambiguity about which ocean it is in.)

It is not Sentosa, Réunion, Al Hallaniyah, Komodo, Java, one of the Maldives, or one of the Andaman and Nicobar islands. It is not in the Arabian Sea or the Bay of Bengal. It is not African or Australasian, or in the East Indies. It is not a British Overseas Territory.

I will tell you for free that I think you are unlikely simply to guess it without more information. I don't expect everyone here to have heard of it (it may fail the Rosie test) but I would expect some or several people to have done so. It does have a couple of claims to fame. And there was a reason why I chose it as a subject; it's not just some random small island.