Pluck off a quantity of the fuzz, and put it in bleach. If it’s wool-only, or blended with silk or oil-based synthetics, the fuzz will completely disappear. If there’s some trace fibre left, it’s blended with a plant-based fibre.
I find wool-cotton blends to be rather heavy compared to pure wool or other wool blends, and they feel cooler to the touch. YMMV.