The DSP in the cart is used for graphic effects not for sound.
You don't need the outrigger connectors for DSP1-4 games, including Mario Kart.
What unit are you running? Some will allow you to pass thru DSP commands to a DSP cart on top and others won't. Since yours doesn't have the outrigger connectors I'm guessing it's an older unit. It may not pass thru the DSP commands to the top slot. Bung had this problem with the GDSF7 and the way they got around it was to put a DSP cart on the bottom, between the SNES and the GDSF7.