If your cousin is currently in the US and has a US mailing address he should be able to join AAA. Note that you should be able to make the reservation on the US or UK booking site, but I'm guessing you want to make it on the UK site for the added insurance. I'm not sure it's "risky" as Hertz's system will accept the age waiver, and the agent is unlikely to challenge you.

One way to significantly reduce the chance for a problem is to have your cousin sign up for Hertz Gold as there's less scrutiny that way. Typically you wouldn't even have to stop at the rental counter, but if it's your cousin's first rental, he might have to stop and show his credit card the first time, but regardless, as a Gold member, there less attention paid in general. Renting at a large airport location is another way to improve your odds.

AAA does have reciprocity with international clubs, so theoretically you could join one of the UK clubs and be eligible to use the AAA discount code, although this is a bit of a gray area, and there are possibly going to be people who respond to this thread and say that's not kosher. Honestly though, either approach is likely to work as the chances of being challenged are low.

Lastly, given that these are the only viable approaches we're aware of for waiving the underage fee, you really don't have anything to lose, other than having to end up paying the fee, so it's pretty much all upside and no downside in our opinion.