Just walking out on the mountain and strapping in won't work very well. Especially if you have no prior experience with anything similar. Try calling the mountain and seeing if they have any late slots or if any of their instructors are allowed to stay late and teach. If so, you may need to pay a little more but it could work.
If not, you could always try to get acquainted with someone who knows how to teach and pay them "unofficially". lol