Well, actually, the Windex wipes are apparently only water, polypropylene and isopropyl alcohol. Still probably not the best thing to use on all plastics.
I found the info below from a PDF that the Office Depot web site shows about them.
Chemical Name CAS-No. Weight %
Water 7732-18-5 60.00 - 70.00
Cellulose 9004-34-6 10.00 - 30.00
Polypropylene 9003-07-0 5.00 - 10.00
Isopropanol 67-63-0 1.00 - 5.00
No idea what's in the OP Wishy Washy wipes, didn't find anything about them. I would guess basically same thing, meant to dry off immediately after wiping.
Maybe that stuff is alright once in a while, not sure about it myself.
Not a lot you can do without water, unless carrying some like RBinTex said. Maybe carry a zip-lock bag with wet soapy cloth that won't dry out? Just have to be sure to finish with clean dry towel.
At home I only use a couple drops of dishwashing liquid on a wet microfiber towel after presoaking with lots of warm water, rinse and dry.