It was Paul Vance. There was an impostor (Paul van Valkenburgh) who died who had claimed to write the song, but the real Paul Vance is very much alive and living in Florida. Paul Vance wrote this song when he was a young man. He wrote it when his two year old daughter was afraid to go into the water in her new bikini. He does continue to collect royalties on the song, and is rightly credited for writing the song and has the gold record it earned him hanging on his wall.
