I was wondering about a Prom on a Thursday too, but I guess different strokes.
I only wanted to say that doesn't have to be that weird, does it? People set other people up all the time.
When I was 19, I had a 17 year old guy friend who was in a military boarding school for boys. He didn't know many young ladies but really wanted to go to his Prom (I don't think they called it that, but whatever). He begged me to go.
No thanks. I was oogied out by the thought of an older woman showing up at a Prom and besides, I had my own boyfriend who would have frowned on it, going as "just friends" or not.
So I set him up with a local girl his own age. I told her that I know it sounds weird, but there's this guy, yada yada, gave them each others phone numbers, and they decided to go ahead and go as "just friends."
She was really nervous about it, but it turned out fine in the end and wound up being really good friends for a while.
Best of luck to your son and the Prom girl.