Truman's decision was to not do anything.
FDR ordered the nuking of Japan before he died. Truman didn't even know of the bomb's existence until after he was sworn in. The decision he took was to not interfere with the orders FDR already had given.
So we nuked Japan, not because Truman ordered it, because his signature did not appear on any of the orders. We nuked Japan because Truman elected to do nothing and let FDR's orders be executed as he'd written them.
It has been a long time since I read the book and I don’t remember a lot of details, but my recollection was not as you portray it. He was President. If he wanted it stopped, he could have stopped it. Even inaction is a decision.