Nairo had quite a few different punishes for ZSS, including fair, nair into combos, bair, and even Flip Kick. Uair and Boost Kick were the most common, but that was hardly the only technique he relied on even for kills.
Really, you're quite underselling how well Nairo played just because you don't like the character. He aggressively pressured him and his shield, covered many of Zero's options, and made sure to pull some surprise mix-ups and KOs that Zero didn't expect. Ultimately, Nairo made sure to utilize all that ZSS gave and played her to a great extent, he didn't rely only on one combo and saying he did severely undercuts how much he put into those sets.