The first option is to take a Dremel tool and carve a grove in a flat head bit so the prongs of the bit can grip the screw head. The second is to take a cheap pen you don’t use anymore and heat the end with a lighter and press it into the hole once the tip is thick but not liquid.
While blowing air with your mouth might work on occasion, the moisture from your breath will eventually ruin the cartridge.
Do not use soap on your NES cartridges.
Don’t go so light on the alcohol at this point. Be sure to wipe away the alcohol before moving on. After that, take your eraser and rub the contacts two to three times. Take a business card and put it between a piece of 800 grit sandpaper and rub the contacts three times in the same direction on both sides.
Dispose of the cotton swab when you’re done.
