First thing first, undress your doll and remove the wig. It will be a lot easier to do all the work without her long tresses, and you'll be taking the wig off by the end anyway.
Now that the wig is gone, I took two plastic store bags and put the doll in (feet first), tying them around the neck. This protected the whole body and leaves only the head sticking out. Your doll should look like this:
https://islandshiregazette.blogspot.com/2019/05/success-removing-nose-scratchesscuffs.html
If you have American Girl dolls, micromesh is something you need. Whether you collect them, play with them, restore them or customize them -- this stuff will be your friend! It removes shine marks, scuffs, scrapes and even cuts! The entry linked above will explain all about it, how to use it and give links for purchasing a nice, inexpensive starter pack.
The micromesh was exactly perfect for removing the eye makeup without damage to any other part of the doll. I used 1500, 1800 and 2400 -- starting with the 1500 and working up. Nanea dolls have a slightly matte finish compared to some other dolls, so you don't have to use the really fine micromesh, but that varies by doll. You just want to be very careful not to let the micromesh rub on the eyeballs, eyelids or eyebrows -- it will remove the paint on the last two and cloud the first.
Start with the 1500 micromesh to get the darkest part of the paint off (always being careful of the eyeballs, eyelids and eyebrows). Once the paint appears to be fading, you can start using the 1800. I swapped between the two for a little while. Once all the eye makeup was gone around the eye, I went back and forth between the 1800 and 2400 until the shine on the vinyl matched the entire face the way I wanted.
Here a couple of pictures that show the doll after about fifteen or twenty minutes of work. You can see that the eye makeup is removed from the left eye.
When you're finished with the makeup, it's time to give your new fellow some hair. What I used on Benny was a Monique "Johnny" wig (10-11") in Dark Brown. This little fellow got the same style, but I'll tell you that the black version looked amazing on him as well! These wigs look best on these boys if you give a little trim at the back of the neck to remove the small curl there.