Straw hats were a feature of hot weather kit going back to the 1850's at least. I've seen images of sailors, on land, in the Crimea in white uniforms with straw hats, different design, larger brims.
Sad about your man, discharged unfit and evidently a victim of the 'Spanish' influenza of 1918/19. Didn't take long to reach Canada did it. Killed more people in Europe than the Great War you know.