I don't think he would've responded to being taunted as short, he wasn't THAT short a man and most of his supposed hatred of it being brought up was British propaganda.
But, if you said to him "The Royal Navy's Better than Yours" or "If you're the Supreme Ruler of the continent, why don't Muscovites obey you?" you'd probably get him wound up for days as he DID have a towering ego. It's just that someone making fun of his height wouldn't likely' set it off.
He was literally a cuck. Ask @TheRealNapoleon about Hippolyte Charles.