Or would I have one? Was there a political figure whose name was shorthand for “a real evil piece of shit” whose invocation would be generally understood to mean the same thing?
This would depend heavily on where you were. In large parts of Europe, Napoleon would be the 'evil dictator' archetype, and in 1925 the German Kaiser would also be extremely unpopular. Although more in a 'defeated enemy, relegated to history' kind of way than as an evil scheming genius. Napoleon definitely had that 'danger to the world' vibe going.
It is worth noting that anti-democratic movements were quite popular in this era, and authoritarianism by itself didn't have the reactionary tinge it has today. The Italian fascists were considered progressive and innovative. They had the support of intellectuals and futurist artists.
Throughout Europe, this was a period of political turmoil, in which one faction's hero was the other's satan, so it would be hard to pin down a single hitler-like figure. Society was also very stratified, with huge wealth gaps, and the resulting conflicts and oppositions. Communism would be a very real threat to any conservatives, large business owners and the traditional ruling class in most countries, so they would also be demonized as harbingers of chaos. In /r/propagandaposters you can regularly find political posters from this era warning workers against the dangers of Communism. A globalised 'workers revolt' was a real fear. The events of the Russian revolution were still very fresh in people's memories, on both sides.