You didn't seem nervous to me. But it's true that you could work a little on the delivery. You actually seemed too relaxed about it, and as a result not paying enough attention to the delivery.

For example:

"What's a little myocarditis when... when Applebees are at stake?"

should've been pronounced without the hesitation, and in a shouting voice. That's okay to do when it's a punchline. It would've been great that way.

I think I know how it works with the hesitations. You didn't forget the line, but you want it to sound naturally and therefore allow there to be pauses, right? But even though it seems tolerable to you, it's always better to have fewer pauses.

(I'm just trying to give pointers. It'd be awesome to see you work on this because I think there's great potential here, you do come up with good jokes.)