The modifying word you may be looking for could describe the source of the fleece used in the wool. Soft wool comes from baby alpacas, llamas and yaks. There may be other sources, depending on your definition of 'soft'.
Any fine wool can be used to fabricate a shawl: a lace weight or a finger weight would be the finest.
pangkuskos
The Tibetian goat grows the finest wool, called Cashmere.
Steel wool
wool feels like soft white stuff. and it looks like well wool
The Indian shawl is commonly known as the "Pashmina" shawl, which is made from the fine wool of the Changthangi goat found in the Himalayas. Pashmina shawls are renowned for their softness, warmth, and intricate handwoven designs. Another famous type of Indian shawl is the "Kashmiri shawl," which often features detailed embroidery and vibrant patterns.
shawl
The shawl Athena wore is called a toga. ( pronunciation... toe gah )
Angora
I believe you are talking about fur. hope this is helpful in some way! ^-^'
sheepskin is soft warm and durable
The wool feels soft.