Merchant navy is more difficult to trace, unfortunately, and difficult to do online:
http://www.nationalarchives.gov.uk/catalogue/RdLeaflet.asp?sLeafletID=128Or if he was registered in Canada:
http://www.collectionscanada.gc.ca/genealogy/022-913.006-e.htmllooking at freebmd, marriages of William L. Cross:
1912, to Alice H Radmall, not him, this family were still having children into the late 1920s.
1913, to Constance A Downing -found one likely child, but was a daughter, no early death for Constance.
1917, to Emma B Bradbury - at least one likely child, a daughter, no early death for Emma B.
1918, to Edith E Walters, in Sculcoates - there is a son, Frank L, b. Sculcoates in 1919. Didn't find a death for Edith, either, but who knows.
The 1918 one looks the most likely, but that combination of names doesn't seem to be rare enough to pin them down if they moved out of the area after 1919.