Oxalic acid is a good all around cleaner. It is a VERY mild acid. You can get it at hardware stores anywhere just look for "Wood Bleach" It comes in small plastic cup sized containers. It is a dry chemical that you mix with water. I have used it for years to remove the stains in hull gel coat from the water of the ICW. One container has lasted me several years.
Not knowing the source of your stains, there is no telling whether it will do any good, but it will come in handy in the future for cleaning the ICW mustache. I don't believe it can hurt anything. Try it on a small area and let me know.
Generally, no scrubbing is required. Just wipe it on and give it a few minutes to react with the stain. I then rinse with fresh water to neutralize.