I have washed my hubby's green beret successfully a few times, also made of wool, but it does have a leather rim band. Advise luke warm water a small amount of Woolite( sold in Tesco) do not leave to soak and press between towel firmly to get as much water out as possible. What is very important to stop it shrinking while drying is to place it on an item the same diameter as it is before washing. If it's very precious to you why not go along to a dry cleaners and ask advice and if they can quarantee it won't shrink then perhaps it would be best to let them clean it for you.