You do need a Uchi I'm afraid. I looked it up and it does seem like it is only Uchi personality villagers who ask for a Windmill. But don't worry, hopefully you can get one without having to let go of a villager you like.
Not just WIndmill! You won't get Picnic Blanket or Wisteria Trellis & a few other things as well. I find Agnes & Tammy to be super cute Uchis but that's just me.
Luckily, I have a Uchi in my other town. I justed wanted to have a Windmill in the town of Dudley.
I love all my villagers in Dudley even the cranky ones and I will not let them move out.
After I found out about the Uchi/Windmill connection --- I sent letters to all my villagers stating I was extremely depressed and I wanted a Windmill. Maybe the villagers (developers of the game) will surprise me.
One unusual thing happened earlier and has never happened before.
Zell requested something and the townhall is closed for the Autumn Moon. I have never had a villager request something when the office has been closed.