Thank you @gcb and @Julien for your replies and suggestion of using a third-party app like Joy2Key.
I also read in a previous thread on this topic of people using a program called antimicro which seems to perform a similar function.
I suppose that will be the route I have to take to get this generic SNES-style gamepad working. I had hoped to avoid the hassle of mapping gamepad inputs to keyboard shortcuts as I had read CM now recognizes controller inputs natively. Ah well!