John Hinkley, Jr., who shot President Reagan, also was not executed by police or the Secret Service. Indeed, he received due process and it turned out he was mentally ill, and he was incarcerated and treated accordingly.
Both McKinley's and Garfield's assassins received trials, and were executed after due process of law. Lincoln's assassin, John Wilkes Booth, was executed in a farmhouse by a soldier, Boston Corbett. Although Corbett claimed Booth drew a gun on him, Corbett's superior reported he shot Booth without pretext. Corbett was arrested until public opinion forced his release.
Even going back to one of the first attempted assainations of a President, a shooter who fired two pistols at Andrew Jackson both of which misfired, due process was given. The would-be killer was found not guilty by reason of insanity and confined to a mental asylum.