I do that, wash, dry, quickly put on hanger, shake hanger, and that's it. I've about eight linen shirts, a few from back when I had some money, but even those on sale, and five or more from thrift stores in California. (Haven't seen any at the goodwill here.)
I have had a friend who was a single guy, movie director and writer, who would only iron if his life depended on it, and wore absolutely totally wrinkled shirts routinely. That was also around the time I started to like "patina" in my worldly goods, like wallets or furniture. So.. I started to have more humor about wrinkles in clothes or on people's bodies, including my own. Patina, that's it.
Anyway, I still try to be relatively unwrinkle-clothed, but keep my iron for a rainy day in 2025.