If it were safe from retrieval I am pretty sure they would let someone know. Certainly other governments would be interested in insuring there was no leakage. Both the US and Russia have lost nuclear submarines and those are well known and even checked for issues by nearby nations.

Now during the 50s and 60s all bets are off, but I doubt any weapon declared one way or another fully escaped attention for this long. You want a real scare, go read up on Operation CHASE which where they were dumping even chemical weapons into the sea

Oh, I know of CHASE. Consider however that they didn't know exactly where it was. In a marine search in such relative proximity to Russian waters, they might not have found it first.

It may well actually be a dummy, but based on their track record I see no terribly good reason to treat them as a credible source.

It didn't later emerge, it was reported by an Asst. SecDef who didn't consult the facts and has been completely disproven. The device was equipped with a simulated trigger and can't undergo nuclear detonation.

The USAF has very little reason to protect this information, and these records have all been subject to extreme and intensive FOIA requests.

They'd tell the Canadian EOD team at the very least. The boys on the pointy end of the stick need to know what they're potentially disposing of.

It's not entirely clear whether the cores were dummies in either case although it sounds plausible. When actual nukes were dropped as in the Goldsboro incident, the government didn't claim the devices weren't fully operational weapons, just misstated the risk of detonation.