I did a quick pitch for GiveWell after winning a gaming tournament, though I had more time than it sounds like you will.

It might help if you can link to a clip of what someone's personal intro sounds like / how it is presented.

In your place, I'd avoid trying to say anything about AI risk in 25 seconds and stick to "effective altruism" (someone who's curious can easily Google that and find out about AI and other things quickly thereafter).

So maybe something like: "I study artificial intelligence and think a lot about effective altruism, which is the art of doing as much good as you can with your money and your time. Google it!" (That last bit may be too much, but I think it could work in the context of a lighthearted show.)

And if you win money: "I'll be donating this to X, which does Y".

Well done and good luck! I generally agree with Aaron. I would say something like: Hi I am x, I do x y. My hobbies are (ideally something relatable, interesting and/or funny for the audience). I am interested in effective altruism, which is.... As part of that, I try to give 10% of my money to effective charities

Other suggestions:
Smile and engage listeners upfront
Don't sound like an ad
Sound relatable and humble and not preachy/morally superior. People are most influenced by credible & similar sources  

I would avoid mentioning EA, it seems hard to get across nuance in 20 seconds and there seems to be a lot of misinterpretation even in longer form media.

Mentioning what you study/plan to work on and where to donate seems like a fine thing to do.

Thank you all for comments! Filming has been delayed until April/May 2022, so have a good five months to consider and also practice my quizzing.

My feeling at the moment is to keep it simple and positive (e.g. 'I have recently become really interested in effective altruism - which is about trying to have as positive an impact as possible with your time and money - I joined a community of others thinking and working on the same thing ~4 years ago and love it') - allowing people to look up effective altruism if they are interested but not going in to much detail about methodology.

I think the positives of this: some people looking up / getting involved with EA, outweigh the negatives: reinforcing negative impressions or spreading a low-fidelity message which prevents proper understanding later on. But would be really interested if anyone disagrees with this/has examples of this kind of messaging not working well(or also examples of it yes working well).

Brainstorming some concrete wording for a personal intro:

"Hi, I'm Patrick. I'm currently pursuing a master's degree in artificial intelligence. A startling fact that keeps me up at night is that humanity spends more on ice cream every year than on ensuring that the technologies we develop do not destroy us. I intend to help change this with my career and with the Giving What We Can pledge I've taken to give 10% of my income to whichever organisations can most effectively use it to improve the lives of others, now and in the years to come."

(The hyperlinked text is taken verbatim from the sources linked.)

The thought behind this wording is that it ensures you actually introduce yourself, but also manages to subtly fit in two plugs--the first being that if a curious viewer tries fact-checking the ice cream factoid by Googling something like "humanity spends more on ice cream than technology not destroying us" the top search results will all be about Toby Ord's The Precipice, and the second obviously being GWWC / effective giving.

If you're thinking about something about GiveWell a catchy line might be something like: 

"The best charities are 100 times more effective than others, GiveWell is a nonprofit that finds these charities and recommends them so your donation goes the furthest (or so your donation can save the most lives)."