Actually I don’t find woodshavings, or straw, to be an issue when prepping a fleece for handspining. Hay seeds are much worse, and the sticky burrs of cleavers and burdock are by far the worst things, along with any thorns they pick up if they have access to hedgerows.
But if you might want to sell the fleeces, or send them off for processing in some way, then yes, VM (vegetable matter) could be more of an issue.