Hi Laura

The Merchant Navy and Royal Navy were separate. Merchant seaman worked for the ship owners, the others worked for the Crown.
There was a separate death index for people
lost at sea but if someone died aboard ship the death would be registered in the normal manner when the ship hit port. An ancestor or mine was lost off the Cumbrian coast, but doesn't appear in either index.
If your man's death was registered in Whitehaven, it need not have been related to his job. If the story didn't make the newspapers, I'm afraid the death cert would be the only way to find his cause of death.