What transpires is really not that embarrassing, at least not in the way it's meant to be:
C'mon, he knew she'd hear him say that she's beautiful. It's a faux embarrassment. A fauxbarrassment.
Dude knows how mics work. He may also know it's gross to hit on someone while they're at work, as this stenographer is. Yet he's found a decent loophole here and for that I respect him.
{Fart noise.}