We will never know will we? Would it have been enough to drop one somewhere nearby after letting them know where to look?
Technically speaking, we could have blockaded the whole Island. Our Navy was astoundingly huge at that time, it would have been a trivial matter to do so. People speak of how we only had two bombs, so we had to make them count. I cannot remember the exact count, but we had more bombs in a relatively short time. The main question, is did we do it to subdue Japan, or to intimidate Russia?
Sage nailed it.
Edit - There is an upside, those little dinky A-Bombs were so horrific, that no one has used one in anger since. Let's hope that continues.