Oh yeah! This is a good one, I have a lot of headcanons about this. I may even include some fic concepts so someone else will write it for me lmao
1. First things first: element HCs
Ranma would be an airbender
Mousse and Shampoo would be waterbenders
Ryoga would be an earthbender, Ukyo is from the earth nation but not a bender
Akane, Soun, and Genma are all firebenders, the other Tendos are non-benders from the fire nation
Obviously, this means Cologne would be a waterbender while Happosai is a firebender
2. Next, the AU would take place more in the LOK time, making Ranma one of the “awoken” airbenders.
3. Following the LOK thing, the Tendo family would live in Republic City and Akane is on a pro-bending team (it’s not the best team, they don’t win too often)
4. The Tendos used to live in the fire nation with the Saotomes, but moved after Mrs. Tendo died. Genma brings Ranma to Republic city so he can be trained, but they traveled around the world before that getting into a lot of trouble. (i.e. Shampoo)
5. Ranma knows fighting styles from all over the planet, his training starting in the fire nation where he learned techniques similar to Ty Lee’s and his airbending movements typically look more like firebending
It’s always difficult for me to separate the original characters from their universe, so this is more like a crossover than an AU, but there’s no reason not to replace them with Ranma characters. I just couldn’t imagine Ranma as the avatar! Who would you have the avatar be? Maybe Kiima could be Korra? I can’t think of anyone good enough to be an Aang replacement lol