First of all, Nail Polish comes in 2 types: Acetone based, and acetone-free. The latter is based on Ethyl Acetate filled up with alcohol and water. Sadly, Ethyl Acetate also dissolves ABS, so it is not an option. However, the acetone-free nail polish remover can be used to smooth PLA to some degree. Anyhow, we look for something that is putting Nail polish into solution but not ABS, so it can neither be among the able ketones (like acetone), nor an acetate ester, nor be aniline.
Next up, Turpentine. Turpentine is a crazy mix of chemicals that we know to be able to turn most glues to goop and remove nail polish too. Sadly, Turpentine too can dissolve ABS, and it has been used in this fashion to create ABS Slurry/Cement as a bonding agent.
But what do we actually have in nail polish that needs to be put in solution? Well, to a good part, most nail polishes are a Nitrocellulose lacquer. To keep it in solution, Ethyl Acetate (already ruled out) and Butyl Acetate are used. Sadly, that is an acetate ester, so nope, no gains here.
So, we are left with one way: Mechanical removal. Nail polish is known to bond quite ok, but conventional nail polish lacquer (not the gel stuff) also is known to chip, and we can use that. Letting the lacquer harden and then using a sharp knife o remove most of the surplus, then polishing it up to very fine 1000 grit sandpaper is a possible way to go without needing to open the chemical toolbox. For the last postprocessing step, very short exposure to acetone vapor should restore the surface and put it to shine, including the lacquer.
An alternative might be other filler materials. For a white filling, white Valejo putty might work, which is an acrylic bound marble dust filler, which can be wiped away with a wet cloth. It doesn't shrink, so gives flat surfaces. It could be colored with other acrylic paints, but the base color is marble-white.
Tamiya Basic Putty is based on Ethylbenzene and often used with ABS models as a gap filler. It is available in several colors. As a downside, it does shrink a little during bonding. Ethylbenzene is not a solvent but incidentally, the same stuff that is used for making ABS so should be safe for the model.