You can wash wicker as long as it's decent quality. Take it outside, use something like dilute baby shampoo or soft soap, warm water and a soft brush, do it quickly then rinse well with a hose and let it drip dry upside down over a big plant pot. Don't put any sort of pressure on the sides when wet or it will deform. It won't hurt the basket to get wet...I make baskets as a hobby and the wicker has to be soaked for several days to make it pliable enough to use, plus old baskets actually benefit from being left out in the rain for a couple of days.