Whether or not Jon should have panicked, "don't panic" were the words (s)he had thought to (her/him)self. Jon was supposed to be good at keeping the disguise, right? So in the new reality, Jon would have been keeping track of his/her period and been prepared. Therefore, Jon must have a tampon available. Or whatever else girls use.
Jon quickly got up, took his clothes the bathroom, and looked through them. His guess was right--he did indeed have a tampon. And, somehow (or perhaps because of the wish) he knew how to use it, which along with a change of underwear solved half the problem.
Now, the other half was the spot on the sheets. If wasn't a big spot, but still was a dead giveaway. Maybe he could spill something else on top of it? The trouble was that there wasn't anything he could spill that would make sense to have and was guaranteed to cover it.
Everyone else was still asleep, but Jon walked over to Karyn and nudged her. "Zzzzzzz..."
"Hey, Karyn, I need the stone."
"Wha? Oh, it's you, Jon... Don't wake me up like that... what do you need the stone for?"
He held up the disposable tampon wrapper to Karyn, not wanting to risk anyone hearing about it.
Karyn couldn't help but smile a bit at Jon's problem, but then said "Lean down."
Jon leaned, and Karyn whispered in "his" ear "You told me you didn't want to use the stone for every little thing. If it doesn't work I'll give you the stone, but first, why don't you try....."