I needed to set up a blueprint actor with some Physics Constraint components that have fixed rotation and keep the shutters attached to the window frame. There are also Physics Thrusters attached to each of the shutters, which are basically applying force based on the Directional Wind direction and strength, which fakes the windy effect that I want.
I decided to keep one of the shutters fixed in the end, as if it's being held back by the ivy that is growing over it, whereas the other one is able to rotate freely.
Next for this is to add some collision effects such as impact sound and crumbling paint, and maybe try setting up some more clever wind which would shoot some rays at the direction it's blowing and only affect the objects that the rays actually hit i.e. if the wind is blowing from behind the house, the shutters wouldn't be affected because the rays would be blocked by the collision of the house.