You don't wash higher than Base Camp, as there are no facilities and it is too cold.
On top of this, you'll need a second set of everything. At the end of a day's climbing, wet clothing is dried inside your sleeping bag while you sleep, to be worn the next day. You don't wash higher than Base Camp, as there are no facilities and it is too cold. The best you might manage is a rubdown of your feet with some snow.