If your partner smokes outdoors and then pets the cat, aside from the smell transfer from the hand to the cat fur, I don't see any health risks to the cat.
But your partner should wash his hands JUST BECAUSE you asked him to, period.
Let's be real - the hands of a cigarette smoker smell bloody awful. The transfer to the cat makes the cat's fur smell. It is not at all a big deal for your partner to wash his hands.
You are NOT being unreasonable at all.....your partner is.
He is acting like a stubborn child and needs to be punished. Maybe you should withhold something from him.
Good luck.