Opening with "I know you're busy" signals neediness and low status. Instead, create something for the person you want to reach, send it without asking for anything, and stay quiet. If they bite, you have a client. If not, you've built proof of what you can do.
Chapters
I know you're busy, let's cut to the chase is a horrible way to start a conversation. You don't start like that because you put yourself at a lower status than the other person. Instead, if you really would acknowledge that they're busy, they probably have money, right? So instead, if you're a beginner, I would take the extra mile. So if you're a writer, I would write some stuff for them and say, hey, I wrote this for you, you can use it if you'd like. And you don't ask, you just shut up. If you think you can make better short form than them, just edit a few videos for them, send it, shut up, don't ask. Because then you will stand out because your competition has one word that's describing them, and that's needy. They're needy as fuck. So you don't do that. You just share what you can do. If they accept it, great, you got a client. If they don't accept it, cool, you still got proof that you can use on other people. Think about it, play the long game. Speaking of playing, you can also play the right game by following me and learning how to monetize your audience.