Big breakthrough on the "wool" front!
I just found this with regard to Goat Hair (hairs from the outer coat): " The yarn is akin to linen, strong with very little elastic memory. "
I am now confident that this is close to the Saetae that Vegetius was describing, as such qualities are quite favorable for slings. The structure of the fibre, along with the natural oils present, makes it durable and very resistant against rain.(as it was when it was on the goat!)
I also found this somewhere else: " Columella stated that it was used for ropes with a reputation for lasting longer in water than hemp ropes, as well as for sacking, sails, and tents. "
https://sciencepress.mnhn.fr/sites/default/files/articles/pdf/az1993n17a5.pdf