Carry a large ShamWow towel and use it as a clothes wringer. Wash out your t shirt, sox, etc. Roll ‘em up in your handy dandy ShamWow and wring it out. Unroll The articles of clean clothing are nearly already dry! Hang in the sun for a bit or tie to backpack and voila.
Learn more about Sham Wow at their site.
Try this one. It may be one more thing in your pack, but it is a multi use item so it works for me!
Have a Great Scouting Day!