Your best option is to get an SNES/N64/GC S-video cable, and use a third-party s-video to component adapter.
The system came with a stereo A/V cable (red/white/yellow), and Nintendo also sold a first-party S-Video cable. SNES, N64, and GC used the same multi-out port, so if you have trouble finding an SNES S-video cable, try searching for N64 and GC S-video too. (GC also had a separate port for component video output.)
Note: the multi-out port on the smaller, redesigned SNES model will not work with the S-video cable. If you only have the redesigned system you'll need to use a composite-to-component adapter instead.
Nintendo has two forms of revision numbers that they use for their cartridge games. The first one is the "-n" identifier on the end of the serial number which means that something physical about the cartridge has changed. In 99% of the cases this is an update to the label.
Back in the mid-90's we saw a lot of "-1" games appear because common games that everyone wanted to buy were being distributed when the ESRB was being instituted. There are many games that have a standard version and a "-1" revision simply because the ESRB rating was slapped on the label.
Nintendo's own Player's Choice logo is another good example of many label updates that required a new revision number because of the addition of the Player's Choice badge.
What you are really interested in is the ROM version of the game that is on the memory chip on the PCB. For quality control Nintendo does mark their games with a ROM ID on the outside of the game. For any cartridge game with a label on the back (NES, SNES or N64) there is an impressed number on the sticker. For games with only a sticker on the front (GB, GBC, GBA) the number is impressed on the game label, with the exception of the DS and 3DS, which also have the revision stamped on the back.
This number represents the facility/manufacturing line that the cartridge was assembled on. If your cartridge has the first version of the original ROM you will only see the 2-digit facility number. However, if a new version of the ROM was released from the developer to manufacturing, then a letter was appended to the end of the facility code.
The first revision will be an "A", the second revision will be a "B", and so on. If you take a look at these identifiers you can determine which version of the ROM is on your cartridges. If both games have no revision code, or if they have the same revision code, choosing which game to keep is up to you.
The ROM version can be a bigger deal than the serial number variation, depending on the nature of the ROM change. Nintendo has been known to adjust the art in some of their games for no apparent reason. Choosing which revision is a matter of preference.
You may be wondering where to find out information about specific cartridge ROM variations. The best place to go for a detailed log of variations to game ROMs is The Cutting Room Floor. (Beware, this is a blackhole for retro-gamer nerds, such as myself!)
To be clear, this site DOES NOT distribute game ROM files but they have thoroughly documented differences between the software variations of many games, old and new, for Nintendo and many other systems.
The only unfortunate aspect of TCRF is that they do not claim which revision ID stamped on the game goes with which revision detailed on their site. Instead, they just say "Japanese Version 1" or "US Version 2" when outlining differences of ROM versions. You may have to read the details on specific revisions to determine which ones may exist on your cartridges but that's never a difficult process.
Best Answer
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.