Polyester scarves are easy to clean yourself. You can safely wash a polyester scarf in the washing machine on a delicate cycle at 30 °C. It is best not to dry your polyester scarf in the tumble dryer; simply hang it on the clothesline.
These instructions also apply to shawls made from a (mix) of materials, such as:
58% acrylic / 18% polyester / 13% viscose / 7% wool / 4% alpaca
56% acrylic / 29% modal / 7% wool / 4% alpaca / 4% viscose