Ply and hinges would look bad in my opinion. Making operable shutters is a bit of a lost art and is a relatively complicated woodworking project.
There are two types of shutters, generally speaking. Louvered and paneled. I suspect you want paneled.
I'l be very brief on the steps to make them, I suspect you wont have the tools to do it. (panel frame, the simplest)
Build a frame with a top, middle and bottom stile, use mortise and tenon joinery for the frame construction.
Build your panels - There are table saw techniques for 'raising the panel' or you can use a router or a shaper. The purpose of raising the panel is actually to make the panel ft into a groove in the frame.
Wood should be knot free and exterior suitable.
Top quality primer and paint.
Special hardware (hinges) is required for operable shutters too.
Now that I write that up it seems pretty simple.
There are companies that still make these. Google operable shutters.