I’d wipe it with a wet cloth and a little of the soap you bath her with. This is how I wipe down my 5 year olds face. I don’t actually put soap on it
My daughter is 7 months and I usually wash her body with soap but for her face and privates I’ll rinse out the washcloth so there’s very little soap left but not completely gone. We also only use sensitive soaps, lotions, and wipes. We haven’t had any issues.
To be honest with you, I’m in the same boat. I think I will be starting to use the baby soap I use to give her a bath with, burts bees shampoo and wash, beginning with her bath times at night then transitioning to mornings. Throughout the day I’ll just use wipes unless otherwise. Hope this helps.