"Lost at sea" is usually recorded in the parish register with the burial entry, even when not all the bodies had been found. They would list all men lost, and often where - e.g. "off the coast of Scotland".

There were usually decrees [admins] for the families of the men to obtain their assets, and lost at sea would also be recorded there.
[See Brian Lawson's index for a possible will or decree, and also Frances Coakley's site for Admin transcripts.]

But are you certain about those dates you gave? Father dying well before the birth of his son?

Sue