There are many who think we should essentially have no contact with nature except to walk through it. I don't buy that idea. Wash up in that lake or stream - just don't use shampoo or soap.Shake off the water and stand in the sun for a moment. When the weather is fine you'll dry quickly from hiking in any case. I often use any clothing I have as a towel, and let it hang from the pack to dry.
A handkerchief can be used for simple "sponge baths." Get it wet and wipe yourself down, or at least wash out your underarms. The handkerchief should be rinsed out away from stream and lakes.
The Ready Store