If he was a seaman, then the captain would have to register his death. and according to everything I have found to date, that needs to be in the country of his birth.
If I remember right, when I contacted the NI register office, the referred me to the office in Dublin and then to Kew in London as they said all early records of deaths at sea was sent there, not sure if that would be the same for Scottish records. Have you tried NRO Edinburgh?
I have my maternal grt grt grandfather Norman McLeod who amongst his various professions, as listed by his family, was sometimes a fisherman in Snozort Skye. He disappears between 1881 and 1883 (got it right this time