I'm guessing that the classic controller runs at about 3v since the wiimote runs off of 2 AA's. (that's a safe accusation, right?)If you open it up, take some pics for me, there may be some pins clearly labeled as what they are. Then, get some nice 50k ohm or so resistors(complete guess here) and wire them in parallel.(one resistor to each led) Lastly, wire the ground to ground. Take pics, I'll make some bad mspaint diagram.
If the voltage is less then what the led needs, no resistor is required. Although, check places with a multimeter, sometimes there are step up regulators in controllers or the system. For example you can get 5 volts out of a gameboy color, even though it runs on 2 AAs.
I recommend getting a multimeter, that way you can check yourself. A very useful tool.