If the webinar is a recorded event, you could just set up an email using either the champ/challenger tool or the random sample trick in the video.. but you can't embed an event or email program type into an engagement program.
The reason is because usually these types of programs will be a one-time deal, so it wouldn't make sense to put them in a neverending nurturing stream. The whole engagement engine hinges on being a machine you don't have to drive... just throw people in and let them get fed.
We leave all our webinar & event programs as standalone event programs, and if we want to temporarily promote one in any of our streams, we just build a basic email, and put it at the top of our stream (like below) so that it's the next email ANYONE in the stream receives. Then we edit the availability so it automatically deactivates itself before the next cast.
With the champion/challenger method, how do you schedule? I can find documentation no how to choose and clone the challenger (which is weird, why do I have to clone the challenger email. Why can't I just choose it?). What I cannot figure out how to do is ever run the thing? I am sure I am missing something super obvious, but I cannot get to the bottom of it.