I actually just carry a couple of dry face washers around with me and wet them if I need to. You can wet them anywhere - water jug at a restaurant, a bottle of drinking water, the taps in a change room.
That way you dont have to clean out your nappy bag everytime you get home - unless htere is a nappy change of course.
I also still carry some disposable wipes around. Sometimes they are just the thing thats needed in a hurry for cleaning sticky fingers or a dirty table, or even a toilet seat in a public toilet for Jenna.
I use a packet of them every 6m or so, I'm not going to beat myself up on that