the safest way without damaging the paint?
If it is washable paint, a vinegar water solution will work. If not washable, blot, do not scrub.
Danielle, here is one tutorial I think will help you with your project to clean your walls. https://www.hometalk.com/41670664/how-to-clean-walls-without-ruining-your-paint
I used a Magic Eraser. It worked great!
I agree magic eraser works fantastic 😊