If one twilight Zone episode is any indication, why bother. Guy goes back, is unable to:1) Get the Captain of the Lusitania to change course2) Convince anybody in Hiroshima what is going to happen3) Kill Hitler
So he moves back to 1881, hears Garfield was shot. Oh well, too bad. But his book on local history mentions a fire, caused by a lantern flung from a runaway wagon…Out for a walk, he sees a salesman. With a wagon, and a lantern. Asks him to move, salesman refuses, argue, fight, horse gets spooked, runs, lantern flies off.
So the time traveler was the cause, simply a part of history that his own book noted had happened back in 1881.