Helmut Zemo offers some interesting comments about his own modus operandi during the movie.
CAPTAIN AMERICA: You killed innocent people in Vienna just to bring us here?
ZEMO: I've thought about nothing else for over a year. I studied you, followed you, and now that you are standing here, I just realized that there is a bit of green in the blue of your eyes. How nice to find a flaw.
Zemo has devoted an enormous amount of time and research to constructing a viable plan to revenge himself on the Avengers. He maximised his understanding of his quarries, so that he could predit their actions and manipulate them with a degree of surety.
ZEMO: Most of it was encrypted. Not easy to decipher. But I have experience and patience. A man can do anything if he has those.
Zemo's attitude is that given sufficient time and application, he can achieve even quite outlandish goals. His patience and application are his greatest weapons.
To take a real world example, while one might thwart casual criminals with security devices, someone who is absolutely determined to break into your house will almost inevitably succeed in the end.
In summary, Zemo's greatest weapons are patience and application/persistence. He relies on his analytical skills to manipulate others, steering events through preparation and understanding - a 'softer' skillset than the 'clockwork genius' that you posit. Zemo steers events, but does not control them.