What tool did they use to separate wool from the animals?
Prehistoric Textiles: The Development of Cloth in the Neolithic and Bronze ... By E. J. W. Barber, a text devoted to the development of cloth in the neolithic and bronze ages, on p. 261, describes the evolution of Indo-European words related to the shearing of sheep:
So prior to the invention of more modern tools used to shear sheep, the wool was simply plucked or combed off when the sheep began to molt. One can also "pluck" wool from the bushy undergrowth which is the natural aid to the animals, which helps them to complete the molt.
Thus hacking the wool off with sharp obsidian blades is unlikely - one merely waits for the appropriate season, and uses combs and fingers! Modern shearing is more efficient: takes less time, and gets all of the wool in its best condition, but combing and plucking will get the job done.
Alpaca after modern shearing and a trim job!
native american technology "shears" brings up Goods, Power, History: Latin America's Material Culture by Arnold J. Bauer. At page 25 it hints that we don't know for sure:
Just how the fibers were separated from the animal is, however, painful to imagine. Presumably, handfuls of wool were hacked off the creatures with razor sharp obsidian, or perhaps Andean groomsmen or women combed out the shedding hair.
It goes on to expand on how the Spaniards thought they'd make money by selling Old World shears to locals (meaning the locals didn't have any such tools). But then continues by suggesting they weren't as successful as they hoped they'd be, noting that the English had a similar idea as late as the 1820s.