You can hide it for 15 ‒ 20 years, yes

Short answer: Yes, but...

Long answer: Can they...

• "congregate the ships": Yes, a suitable choke point can crowd up the enemy ships, especially if they make a feint that builds enemy confidence that they can pass there unopposed

• "drop the nukes": No need, I would instead leave them as remote controlled mines

• "kill any survivors (if any)": gruesome, but yes

• "clean up the wreckage, and then collect any irradiated material": not a chance, simply too much mass

The obvious place where this will leak is from the staff involved in creating/deploying the bombs. You can keep it tight, but any conspiracy involving two people or more, is liable to leak. The prime example of keeping a weapons program under wraps is Israel. There have been leaks, yes, but very few.

"But what about the explosion, and the resulting radiation?"

Here is the thing: no one is looking for that, at that point in time. No one knows about nukes in general.

And not even when knowing about nukes, and looking for them, can we be sure to actually notice their use. The Vela incident for instance, even though direct evidence of a nuke was captured on instruments, was more of a mystery than a finger pointing at a culprit. And that required satellites to capture!

So, assuming the nation can enrich uranium to make a Little Boy gun-type bomb ‒ a plutonium implosion bomb is entirely out of the question for an island nation in this time-frame ‒ and make enough of them, say 10:ish, then yes, they can conceivably wipe out the invasion force and hide the truth until the 1960s.

• Hostile witnesses of the explosion are eliminated.

• The fallout will be diluted by the time it reaches the major nuclear players, and no one is expecting it anyway.

• The wrecks will remain.... but finding a wreck when you do not know where to look for it, is hard. And the island nation may also cordon off the entire area. (Plot generator!!)

• Since Japan is defeated by the Allies, records of this failed invasion might get lost. There will by much wondering: what happened to the ships? We know they should exist, and now they are just... gone. (Plot generator!!!)

So, without too much artistic license: yes, this plot works.

You can hide it for 15 ‒ 20 years, yes

Short answer: Yes, with some reservations

Long answer: Can they...

• "congregate the ships": Yes, a suitable choke point can crowd up the enemy ships, especially if they make a feint that builds enemy confidence that they can pass there unopposed

• "drop the nukes": No need, I would instead leave them as remote controlled mines

• "kill any survivors (if any)": gruesome, but yes

• "clean up the wreckage, and then collect any irradiated material": no, not a chance, simply too much mass

The obvious place where this will leak is from the staff involved in creating/deploying the bombs. You can keep it tight, but any conspiracy involving two people or more, is liable to leak.

Still though, it can probably be kept tight enough. The prime example of keeping a nuclear weapons program under wraps is Israel. There have been leaks, yes, but very few.

"But what about the explosion, and the resulting radiation?"

Here is the thing: no one is looking for that, at that point in time. No one knows about nukes in general.

And not even when knowing about nukes, and looking for them, can we be sure to actually notice their use. The Vela incident for instance, even though direct evidence of a nuke was captured on instruments, was more of a mystery than a finger pointing at a culprit. And that required satellites to capture!

So, assuming the nation can enrich uranium to make a Little Boy gun-type bomb ‒ a plutonium implosion bomb is entirely out of the question for an island nation in this time-frame ‒ and make enough of them, say 10:ish, then yes, they can conceivably wipe out the invasion force and hide the truth until the 1960s.

• Hostile witnesses of the explosion are eliminated.

• The fallout will be diluted by the time it reaches the major nuclear players, and no one is expecting it anyway.

• The wrecks will remain.... but finding a wreck when you do not know where to look for it, is hard. And the island nation may also cordon off the entire area. (Plot generator!!)

• Since Japan is defeated by the Allies, records of this failed invasion might get lost. There will be much wondering: "What happened to the ships?! We know they should exist, and now they are just... gone." (Plot generator!!!)

So, without too much artistic license: yes, this plot works.