The development of the atomic bomb did more to change the nature of international relations than Truman’s decision. If Truman had not used the bomb then, it would eventually have been used and things would have changed at that point. So, it is the existence of atomic bombs/nuclear weapons that matters more than Truman’s decision.
The existence of nuclear weapons changed international relations forever because it, in essence, made all-out war against a nuclear power unthinkable. Before the development of nuclear weapons, it was possible to contemplate a war that might lead to the destruction of another country. Hitler clearly contemplated just such a result when he invaded the Soviet Union. He could launch that invasion, rationally expecting to be able to win. After nuclear weapons were developed, such thinking was impossible. There is no rational way to launch a major war against a nuclear power. It is clear that if you get to the point where you are seriously threatening that power’s existence, it will attack you with nuclear weapons. A unilateral nuclear attack destroys much or all of your country. A nuclear exchange can destroy all of both countries. This sort of thing is too horrible to contemplate.
Thus, the development of nuclear weapons, in a way, removed war between major powers as a possible instrument of international relations.