Annie Oakley is promptly arrested, tried, and executed, for having "assassinated" the Kaiser.
The American government protests strongly against this injustice.
Arguments go back and forth across the Atlantic, with other countries taking sides in the dispute as well.
Escalation.
World War.
Arrested yes. Probably tried, yes. But executed?
Under German Civil Law you could only be executed for high treason and premeditated murder.
How do you prove either of those here?
Sure, the prosecutor and police will investigate very thoroughly. Political affiliations, unexplained money transfers, things like that.
But she is a foreign citizen, a celebrity and a woman.
Unless the investigation turns up something pretty convincing I don´t think the prosecutor would ask for the death penalty. Even with emotions running pretty high, an accidental killing / manslaughter seems more likely?
And I just have to ask some commenters here?
Why should the actions of one person (not employed by the USA, not in any way connected to the US government) result in an American-German war?
The situation is not comparable to 1914 in any way.