Every class has a job. Overlay is to show an overlay not to hook windows functions.
Hook_Manager's job is to manage hooks and should not contain a reference to the overlay. (It should not contains any reference to directX or OpenGL either but I'll see that later... Maybe)
This makes the overlay code much cleaner and "could" be used in Linux as well.
Some games doesn't initialise Steam before initalizing their Renderer (even if the doc says to) . So instead of waiting for the game to initialize it, hook to the rendering functions and deduce which implementation should be used.