I painted mine without removing them using a special paint made for outdoors. They still look amazing. https://www.semiglossdesign.com/how-to-paint-vinyl-shutters
Here's a post that might help - https://www.todayshomeowner.com/how-to-paint-plastic-or-vinyl-exterior-shutters/
First clean those shutters thoroughly. When they are dry, you can spray them any paint that says it is good for plastic and vinyl.