Are your shutters just for looks or are you going to want to open and close them?
If they're just for looks you can line them up on the windows a screw them fast to the siding. You will want to put anchors in the siding so that the screws don't work and wear your siding. If they are going to be opened and closed you will have to use hinges on them. I'm not sure what kind of hinges but you should be able to look that up on the internet. My shutters are just screwed to the siding and look ok. The thing that I dislike is that wasps and such get behind them where the grooves in the siding don't meet the shutters. I have caulked those grooves with clear caulk and carefully wiped up any excess so it doesn't show and look messy. Has stopped the wasps and kept the moisture out from behind the shutters.
I loved your suggestion!! It was spot on!!
Here is a post that will help. https://www.hometalk.com/38964441/how-to-remove-and-install-shutters