I put lavender oil drops directly on my travel shawl. Pure essential oils don't stain as they are not oils in the classic sense. It really needs to be pure aromatherapy grade oil- I get mine from here: https://www.fragrantearth.com this I feel can protect us from germs to some extend as it purifies the air.Do you put the oil directly on the fabric of your shawls? Does it cause any oil stains?