First, whatever you try, you might want to test it on a similar cartridge that does not have significance to you. That being said...
For some cases, sharpie (or other permanent marker) on dry erase boards can be removed by marking over it with a dry erase marker, then erasing it. I have used this method countless times, and for anything but an extremely old whiteboard, it works. It's also worked on some other smooth semi-gloss surfaces that would otherwise be dry-erasable. Whether or not an SNES cartridge falls into that category, I really don't know, but I'd rather have a big black rectangle/square on a cartridge than some kid's name (worst case).
The other thing to try would be lighter fluid, but I'd only do this in an extremely well ventilated/fan-on-high area, because the fumes could potentially damage the internals of the cartridge. Small amounts applied with a cotton swab. With that in mind, it might be a good idea to cover all of the exposed openings of the cartridge.
Another option if it's still available would be to buy the other cartridge as well, and transplant the good label to the unmarked cartridge. Not optimal, (and definitely more expensive) but could potentially yield the best results if done carefully.