If it's a safety issue, better to ban them altogether. What he said exactly is
But you must buy one of an approved bone conducting headphones.
That reads to me you can use them, but only if it's from a list of approved models.
I went through something similar when I was at the casino. They took away the 5-gallon water coolers we had at each work station because of covid (covid doesn't spread through surfaces, but nobody at the casino ever bothered to learn that). To make up for it, we were allowed water bottles, but they had to be clear plastic, so that we couldn't stuff money inside the water bottle and sneak it out (first of all, ew, secondly, the drawer would come up short if we did that and we'd be caught when they reviewed the tape, so what would be the point). I bought a clear Nalgene bottle, only to be told that it wasn't "clear enough" because it had the Nalgene logo (smaller than a dime) and measurement lines printed on it. (I used it anyway because by that point it was clear that I wasn't going to be able to stand the place for much longer, and now it's my bedside water bottle for when I wake up in the middle of the night.)