Simplistic though this might seem, I don't think things would have turned out differently. In the final analysis, the use of the bomb (twice, to be sure) brought the war against Japan to its quickest end, with the fewest casualties. Many have advocated a demonstration, but the Japanese could have brushed that aside as a one shot, which means that someplace like Hiroshima or Nagasaki is going to be ground zero anyhow, to show that the US wasn't bluffing. And a conventional invasions would have yielded casualties in the millions.
Short version: can't see either Dewey or Roosevelt doing anything other than what Truman did.