I have never heard of washing floss. Lots of cross stitch in my background. I would not take it out of the skein if I were going to. Just gently swish it in a sink of warm water with little soap and rinse. Lay the skeins on a towel to air dry. They are so small it shoudn't take long or ruin the floss. Maybe pull the paper off the end and tape it and a color snip to a paper so you have a reference before you wash it. I don't think it will hurt to wash it except that some colors may run. I have never had this happen. good luck.
peace