Good question. You may be thinking along the same lines as I. I would think if an island disappeared someone would take note of it. If there were such a vanishing island, I would think scuba divers would investigate and find some evidence of a nuclear explosion to substantiate the claims. Since I see no evidence of a disappearing island, or the footprint of an explosion, I find a story hard to believe.
So far as I know, only one island has actually been totally vaporized by a nuclear blast. That was Elugelab, it was obliterated by the IVY MIKE staged-fusion test in 1952. The 10.4 megaton blast obliterated the island, and the water at the blast site actually boiled for 24 hours afterwards. If Japan tested a much smaller fission bomb in the scope of FAT MAN or LITTLE BOY, it wouldn’t erase an island. As for the footprint, it could have been covered over, it could have been altered by erosion, or it could even have taken place underwater in an attempt to hide it from the Soviets.