If we can speculate concerning an Old English element in Elfwine, I still think it's easier for him to have translated the tale of the War of the Ring and Bilbo's translations into Old English...
... and
after this task, now inspired to learn more and actually meet Elves, he sails off into the West -- maybe returning with some of the more purely Elvish-written sources to compare with the largely Mannish and
Middle-earthian Elvish accounts of the Elder Days.
Thus Elfwine possibly returns with the legend of the Awakening of the Quendi for example, in which the Sun already exists when the Elves awaken -- though granted that was said to be preserved by the Sindar as well, in any event. Or a more purely Elvish account of the Downfall of Numenor perhaps (in which the world was always round, as the Elves of Aman teach in the Mannish account). Also, maybe more linguistic materials, or more detailed accounts of the doings in Aman that were not remembered in Numenor.
Or something
Although again, I'm not sure there is any indication that Tolkien imagined this as the scenario.