I have denim ballet flats and the Cles and I wouldn't use detergent...I would use the gentle carpet cleaner, Folex, to clean off dirt spots. I've used that on the zipper pull areas of my Pochettes and it cleans them up well.
i have actually never had a reason to clean my mini lin ebene tanger. i have used it several times on my travels and even used it while raining and the canvas still looks nice. it is quite hard-wearing. but if necessary, ya, baby wipes might do the trick. i wouldn't suggest anything harsh like detergents, it might just get worse. good luck!