PVP is great for desinfecting wounds and for cleaning skin around wounds to prevent contamination.
Benzalconium is great for cleaning hands before cleaning wounds, but can be applied to wounds too. Personally, I am not crazy about this one.
Alcohol can be used for both hands and wounds, but it stings and kids don't like it that much.
Consider adding some Neosporin packets to your kit for wound dressing and long term desinfection.