I'm going to tank a coworker over a chronic cough
Is that all that is bothering you?
Yes, it's that weird cough that could put me off.
It is rude of your coworker to be disrupting others with this cough, but they cannot control it.  You shouldn't be willing to punish them for this, and definitely shouldn't be trying to harm their employment.
I don't care what happens, I just want him out!
I understand you discomfort at being around a sick person, but there are steps you could take short of sabotage. He's obviously sick and shouldn't be at work. Why not talk to him, your manager, or Human Resources?