forgive me for not engaging with your core ideas, but as far as I know the vernacular term is "cattle prod" and "cattle prick" sounds rather like something else
No cattle prod is something that a person weilds. A cattle prick is attached to a load like a wagon behind the animals to poke the animal to get it to keep moving faster than the load.
Edit: I guess formally it's called a goad
https://en.m.wikipedia.org/wiki/Goad
The phrase I'm pulling this from is "don't kick against the pricks"