Okay, since this is just a month old and no other people have commented it seems fair to add a little speculation, partly for help in case I ever start one TL I'm thinking of with a POD of Taft on the Supreme Court in '06. (Well, that's the main one, the POD is actually a little earlier to keep him from going to the War Dept. and hence Cuba) It will mean a WW I that starts and ends a few years earlier.
While U.S. troops going over to Europe are said to have begun it, since the first go-around began in Kansas early in 1918, there is also the idea that part began in livestock and there were a lot of animals going over to Europe for foodstuffs.
Given the first, I am thinking that it need not have been soldiers carrying it over. A number of Americans going anywhere could have started it. While there wouldn't be a major war, and perhaps not even an army base at this point, it would begin. Quite possibly Americans delivering foodstuffs to Mexico as they recover from their war might cause it to really get going, then whomever Mexico trades with might get it. Mexican Flu, perhaps?
In the second one, world trade was pretty big, just like today. While people didn't travel as much as now, of course, partly because transportation wasn't as fast, world trade would have been even larger with an early end to WWI as it was OTL. Indeed, one could srgue that U.S. merchants selling food to various places could pass it on just as rapidly as soldiers did OTL. Even a few years later some areas will still be recovering some and will need more imports, after all.
SO, I think it's more that it goes through different vectors rather than it being less severe. And, that the map of where and how it spread would still cover the clobe, it might just go in different routes.