Why is Sylder's toe injury probably unrelated to a war injury?

In this section, Sylder's distinctive toe injury is finally explained. He was shot in the foot some time ago while on a boat. The most obvious interpretation of this passage would be that Sylder was a seaman for the Navy, but the book's time line makes it difficult to place him in any specific war. Given that he was born in 1913, it would not have been possible for him to have served in the First World War (America was only directly involved from 1917 to 1918) and America would only just be entering into the Second World War at this point in the story (around 1941). There were no major conflicts to speak of during the intervening period and, thus, the more reasonable interpretation might be that he was involved in some kind of criminal activity, perhaps smuggling.