Do it anyway.
After hours extra credit :D
I like the way you think. Because it certainly can't be done (legally) in the classroom.
Here's an example. Our physics curriculum handbook (actually it's a big binder), sets out in detail what I must teach every day. No variations permitted! There are no lessons on torque. So I must not teach it! But torque is a key concept in physics.
So I sneak it in wherever I can. Fortunately, most supervisors who observe me know nothing about physics. So I haven't been accused (yet) of "infidelity to the curriculum".
Yes, that's the term they actually use. And it's a firing offense. Crazy.