For what's it worth, way back in New Mexico in the 50s we wore what was then called "fiesta dresses" that had wrinkles by the million in the them. We were instructed to wash them, not wring them out, but to pull them up through a nylon stocking that had the foot cut off. Hang to dry. Don't remember much about the blouse, but the skirt was always wrinkled, and generally strong multi colors.
I think I'd try the scarf wet and pull through a stocking leg. Might work nicely, especially if it's a fabric that wrinkles easily. Sounds like maybe a linen type might wrinkle faster and keep them!!! It does in skirts, that much I do know.