First and foremost, if you "shaved" instead of just "trimmed," there shouldn't be any itching, 'cause we'd be talking about surfaces that'd just had their hair removed. If you've still got short hairs left, get the girliest leg razor you can find, and finish the job. I tested out how easily or not I could cut myself with one of those things on my arm, and I swear to you I'd have to fire it out of a howitzer. Take another pass with one of those in the direction your hair grows, then again against the grain.
Do this the morning before your meeting. If--IF--there are any complications, that should give you time to handle 'em. You'll know you're done when you stretch your legs and realize how oddly pleasant a smooth scrotum can feel.
Everything folks have said about "the future" so far here is accurate as well. Either leave your hair at a moderate length with a trim in the future so that you at least have some good grooming (which is just courteous) or continue to shave completely (which is not only courteous, but for some quite inviting) for some time. Your skin'll toughen up and have its nerves deadened a bit over time and life will make a wee bit more sense.
In the mean time, if you're all out of ideas and resources, MAN UP! You just stuck cold steel to your warm flesh and now you're worried about an itch? Take a deep breath and then take the genitals you just handled into consideration. It just so happens they're not ovaries, so QUIT YOUR BITCHIN'!