- I'm 99% sure it was written by a Russian author (1% - it may have been written by Polish author)
- Author is male (I'm 100% sure)
- I seem to recall the author's name or surname starts with "P", but I may be wrong
- It is probably old (I read it almost 20 years ago, then I immediately forgot the author & title and I've been looking for it ever since)
- I'm not sure it was translated to English (I read it in Polish, 50% chance it was translated, it was really good)
- The main character was a teenage boy and his friend - a dolphin with a translating device.
- There was a sea base they were living in and a slightly (or highly) radioactive nuclear test site near by, there was also a coral atoll (or a coral atoll was a nuclear test site)
- they swam a lot :)
The only thing that comes in mind is "Dolphin Island" by by Arthur C. Clarke. There definitely were translator for dolphins, teenager boy and a lot of swimming. Don't recall nuclear test site though, but there was one episode - dolphins were telling a story about a big object landed into the ocean long time ago, then exploded and many dolphins died from something that looked like radiation sickness.
This sounds a bit like the 1961 book The Voice of the Dolphins, written by American-Hungarian Physicist Leó Szilárd; but it is only a collection of short stories, the eponymous one of them about sentient dolphins. It has been quite a while since I read it last, but as I recall most of the stories were about nearer or farer future scenarios, depicting life on Earth during and after the active use of nuclear weapons. Basically, the stories are cautionary tales against the use of the Bomb.
This topic was important to Szilárd, who is regarded as being directly responsible for the creation of the Manhattan Project, having written the original 1939 draft to the Einstein letter urging US president Roosewelt to intensivy research and development of nuclear weapons. A pacifist at heart, Szilárd later regreted this deeply. He did not write much prose, this is the only book of it I can find. Which is a pity, because I would have loved to read more of it! In case this is not the story you are looking for, I still recommend it. It is an interesting read.
Many, many years later, probably mostly for the benefit of people who find this question via Google like me:
It's likely that the book you are thinking of is by Russian writer Sergey Georgievich Zhemaytis (linked is the Russian Wikipedia article) - either The Eternal Wind (Вечный ветер, 1967/1970), or its sequel The Large Lagoon (Большая лагуна, 1977). They may also have been published under titles such as "The Floating Island", "The Artificial Island" or "Children Of The Ocean". There's also a number of stories that appear to be set in the same fictional universe, but it's unclear if they are included in the larger books.
It seems that The Eternal Wind has been translated in Polish as "The Floating Island", Pływająca wyspa: https://w.bibliotece.pl/5023326/P%C5%82ywaj%C4%85ca+wyspa