Are the huggies baby wipes fragrance free safe for my little girls? Or should I wipe it down with water afterwards?

I do not use baby wipes, worry about the chemicals.
My wife makes up a vinegar and water mix to clean the cages. she find the ratio of vinegar to water on a glider website. vinegar and a spray bottle is also cheaper then baby wipes.
it is strong at cleaning and safe for gliders.

(we rescued a pair of gliders that the owner had used baby wipes to clean
them cause they smelled. the gliders seemed to have stopped grooming and had dirty matted hair. It took months for them to start grooming again.)

Do you mean to use on the cage or on the gliders? I would not use wipes on the gliders. Have you ever licked your hand after wiping it with a baby wipe? They do not want to have to taste that. I believe that may be part of why BYK's rescues weren't grooming.

Most people use hot water and vinegar to wipe down the cage. Don't heat up the vinegar though because I don't think it's good to inhale the fumes.

I wouldn't recommend it.. because I'm not sure with the chemicals if it is safe. I recommend the spray BYK and Scoria are talking about (I use it too) or warm/hot water with Dawn Soap.