The question of whether a "demonstration" could be done was weighed by a committee of scientists and political/military people, and rejected. It was never presented to President Truman as an option (and he did not propose any new options). There were many among the scientists who worked on the project who explicitly argued for this, both in reports, petitions, and polls.

The scientists' argument in the Franck Report was this:

From this point of view a demonstration of the new weapon may best be made before the eyes of representatives of all United Nations, on the desert or a barren island. The best possible atmosphere for the achievement of an international agreement could be achieved if America would be able to say to the world, "You see what weapon we had but did not use. We are ready to renounce its use in the future and to join other nations in working out adequate supervision of the use of this nuclear weapon."

This may sound fantastic, but then in nuclear weapons we have something entirely new in the order of magnitude of destructive power, and if we want to capitalize fully on the advantage which its possession gives us, we must use new and imaginative methods. After such a demonstration the weapon could be used against Japan if a sanction of the United Nations (and of the public opinion at home) could be obtained, perhaps after a preliminary ultimatum to Japan to surrender or at least to evacuate a certain region as an alternative to the total destruction of this target.

So it was basically a "demonstrate before actual use" sort of thing. If the demonstration didn't work, nothing would be lost.

The military guys were very interested in the idea of "shock" though, that the propaganda value would be half of the punch. In any case, they also worried that they just lacked enough weapons to do it like this — they weren't going to make a billion dollar bomb and then set it off in the ocean.

Ultimately it isn't even clear what Truman really thought the bombs would do. Whether he was concerned with killing many innocents is similarly obscure in the records of the time. Would he have chosen a demonstration if the options for casualties had been laid before him? We don't know, we can't know. Would it have had any effect on the Japanese? Similarly unclear, though it might have been hard for the US to play up the awesomeness of the bomb and then follow through with using it on a city — there probably would have been outcry.