The only age-reliant plot points are the Water Tribe's, really.

Aang's story can just be they test and confirm the Avatar at 16 or somewhere instead of as a child. They're ascetics so you don't need to shoehorn in any childhood romances or experience, he can still be "innocent" to those things given his harsh monk upbringing.

Zuko and Azula can just be... older. If anything, Zuko should have been older in the first place, given his relations with Mai.

The water tribe, though, they'd need to explain why Katara isn't pregnant and continuing their very thinned bender bloodline, and why Sokka, son the the lead hunter, is so free to go off and do as he wishes. Do those two plot elements, and yeah, Avatar can be basically moved 1:1 up 10 years of age for everyone.