I've not seen any of those movies that preceded The Cowboys. Of course, I knew Wayne had died in other movies... but as far as I know, Dern was the first point-your-finger-at-him-yeah-that's-the-guy to put The Duke six feet under.
A quick buzz around the intrawebz suggests that even though Wayne was stabbed by a lance in The Alamo, he goes on to use explosives, and dies when they go off. Likewise, though he had been shot, it is an explosion that gets him in The Fighting Seabees, ultimately. Without seeing the movie, I can't tell if it was a sort of suicide mission to crash his vehicle into the oil tank, or if he died from the shot just before the collision, or what?
I haven't found anything specific on the death scene in Sands of Iwo Jima. Is The Duke killed by a nameless/faceless sniper, or does he get some bona fide screen time?