If he was aboard a UK registered ship I would have expected his death to be registered at the GRO. How have you checked the GRO records? If you used an intermediate site like Ancestry or FindMyPast you need to be aware that some overseas deaths are recorded in a different series of records, and you may need to check them specifically.
For example on FindMyPast look in the collection entitled British Armed Forces and Overseas Deaths and Burials.
On Ancestry check the collection UK, World War I and World War II Shipping and Seamen Rolls of Honour, 1914-1945 - this won't give you the reference for the GRO registration but it will confirm that his death was acknowledged by the British authorities and thus there will be a GRO death registration, albeit maybe a post dated supplementary entry.
https://roll-of-honour.com/Databases/MercantileMarineCasualtiesWW1/index.htmlDetails of the deaths of over 15,500 merchant seafarers due to enemy action in the First World War can be found on the Commonwealth War Graves Commission (CWGC) website: cwgc.org
This from the National Marotime Museum: "The CWGC database does not cover all deaths on British-registered vessels, so it may be necessary to consult official log books (see above) and other documents submitted to the Registry of Shipping and Seamen. The NMM holds the following records of deaths extracted from log books of British-registered vessels:
Monthly Returns of Deaths of Seamen (GR160 forms) 1916-1989 numbered with the prefix RSS/A. These provide brief details of the cause of death and the relevant vessel. They mainly record deaths resulting from marine causes or accidents in ports, but deaths resulting from enemy attacks on fishing boats and other small vessels are sometimes included.
Returns of Births and Deaths (B&D1 forms) 1914-1919 numbered with the prefix RSS/B. These records are arranged by month and then alphabetically by the vessel name. They provide more detailed information on the circumstances and sometimes include reports from medical staff, police, etc. There are also B&D1 forms recording births and deaths among passengers on merchant vessels 1914-1919 numbered with the prefix RSS/C.
Registers of births, marriages and deaths of seamen and passengers (including foreign nationals) maintained by the Registry of Shipping and Seamen are in the BT 334 series at TNA. For the period 1910-1918 there are also registers recording births and deaths reported to one of the national Registrars General. The TNA research guide on births, deaths and marriages at sea (Births, marriages and deaths at sea or abroad) provides guidance on the relevant records at Kew and links to resources on the Findmypast website."