I have no idea about an IRL analog of what Malfoy has, but I'd recommend the book The Charisma Myth (in addition to, not instead of lsusr's suggestions), and all types of acting, not just improv. Improv may be great for overcoming shyness and other mental blockers, but acting from a script and inhabiting a character lets you try on vastly different ways of experiencing the world. Playing a powerful and/or confident character won't teach you negotiation skills, but if done right it will teach you the body language of a powerful person and what it feels like to have that mindset.
I mention this because people are really into recommending improv, but I personally have a crippling fear of improv even though I love being onstage. If that applies to you too (the general 'you', not just shenkev), then don't think that all of the benefits of it have to be closed to you – you can get a lot of the same out of normal acting.
The best classes for overcoming shyness and becoming more social are called "improv comedy classes". Unfortunately, improvisational comedy works best in-person. What can you do during this pandemic?
If the core problem is you are shy then that is straightforward to fix. Just do a bunch of low risk (to yourself and others) socially scary things like giving presentations, filming YouTube videos, writing a blog, writing complimentary emails to people you respect, etc. It doesn't matter whether anyone watches or reads these things. The purpose is to decondition shyness and improve your communication skills. Eventually your brain will calibrate itself to the true low risk of social initiative. Pseudonyms are allowed.
If all you have read on this subject is Cialdini's Influences then you have not yet exhausted the trove of useful literature.
I also like to ask for occasional mentorship from a senior engineer I trust and respect, but this option is not available to everyone.
I took a class based on Getting More and it was interesting and useful. This was offered by the company so I can't comment on general classes. There's evidently an online course based on the material, no idea if it's more useful than just reading the book.
I like GM more than e.g. the Carnegie book because it's just usefully framed as "understand what the other person wants and try to get it for them" which is like 90% of being a good negotiator, assuming you know what you want as well.
Consider the option that "negotiation" as a topic is a corporate fad. You hear a lot about it from the kind of people who try desperately to chase some kind of corporate game, but in practice, negotiation skills are not really that important in a work environment for the simple reason that these environments are by nature very cooperative. As long as you can get to clarity with people on what needs to be done, not much negotiation needs to happen. It's quite easy to spot the graduates of negotiation classes at work - they are the ones who waste everyone's time by practicing their negotiation jiu-jitsu moves when everyone else is just trying to agree on a project plan and get working. Maybe it's a virtue to not be one of these people.
I second this. Most negotiation advice is geared toward formal "negotiation" settings, like when you are negotiating sales contracts or business transactions. For those purposes, having negotiation tools is really useful (my favorite is "Bargaining For Advantage" which I learned of from The Personal MBA). But for being a manager, you are almost never explicitly negotiating, and in fact trying to come into your work with that mindset is counterproductive. When you are working with your reports, it would be disastrous. When you are working with other interna...
I think this is the notion of "dark arts" in HPMOR. You don't necessarily become "one of those people" when you learn the tricks. You can choose not to employ them. But I feel like not everyone I meet will be cooperative and that's why it's handy to keep the "dark arts" in my back pocket when I encounter non-cooperative people.
I will add "Never Split the Difference" by C. Voss to the recommendations.
While it's not a class, I found it shifted my thinking in a new direction. The book focuses heavily on concrete techniques, but after finishing it, I came to realize a deeper theme behind all the techniques: getting both sides to talk and reveal their preferences without shutting the door in someone's face. All of the "tricks" are meant to establish a channel (and keep it open) until both sides can figure out a price.
This has also pushed my understanding of conflict from "argh, this means war" to "hey, this is an opportunity to learn what's important to you and me and figure out a way forward that we're both happy with."
I won't be negotiating any thing like a house, car, or salary any time soon. However, after reading this book, I believe I see little opportunities every day to exercise these skills, like when doing sprint planning or trying to dig deep into why a family member is opposed to some course of action.
For me some of the lecture notes from the MIT OCW course "Power and Negotiation" were quite helpful. However, that mostly applied to contract negotations - as others here have remarked, for the internal workings of a company those negotiation skills are much less relevant. For that I would rather look into diplomatic skills, dealing with conflicts etc.
Chad Ellis wrote a good blog about negotiation for many years at http://negotiatewithchad.blogspot.com/.
This podcast series on the Jordan Harbinger Show with Alex Kouts is so useful I would have paid to listen to it:
https://www.jordanharbinger.com/alex-kouts-the-secrets-about-negotiation-part-one/
In HPMOR there is the notion of Malfoy's "negotiation tutors". Are there good classes or private lessons irl that are analogous to that (either online or in-person post covid)?
I'm a shyish programmer thinking about going into a managerial role. Wanted to get a leg-up by training myself to be more social and better at negotiation. I read Cialdini's Influences but theory is no replacement for practice. I'm not sure where to find such classes since a lot of classes online seems scammy/low-quality.