As the talk progressed, I became more and more confused as to how on earth Sleeping Beauty could have pricked her finger on a spinning wheel. Everything is blunt! So I asked.
Our speaker said there were two options he could think of. The less compelling one involves flax. Insufficiently retted flax can have splinters in it, from its pre-retted woody state. So that's a source of splinters, and any complications which might arrive from one, but that's it.
The better option involves wool, whose natural roughness can act as a kind of sandpaper on the wood of a spindle, sharpening it to a point over a long period of use. Unwashed wool, to my complete surprise, can also transmit tentanus. So a wool-sharpened spindle on a Great Wheel (like this one), infected by tetanus-bearing wool could indeed cause a pricking of a finger followed by stiffness and death. I find it both an elegant and satisfying solution!
Sleeping Beauty: She lived before tetanus shots were developed in 1924.*
* Or, of course, much later than that. Invention does not equal widespread availability.