Here are relevant references from the Books where quirts are mentioned.
I make no pronouncements on these matters, but report them as I find them.
Arrive at your own conclusions.
I wish you well,
A young man, blondish-haired with blue eyes, unscarred, bumped against the girl's stirrup in the press of the crowd. She struck him twice with the leather quirt in her hand, sharply, viciously. I could see blood on the side of his neck, where it joins the shoulder.
Nomads of Gor Book 4 Page 67
In her hand she carried a long supple kaiila quirt of leather, about a half inch in width and a yard long.
Tribesmen of Gor Book 10 Page 55
I passed a stall of perfumers, and thought of Saphrar of Turia. Then I passed a shop where the high, light kaiila saddles were being made. One could also buy there saddle blankets, quirts, bells and kaiila reins.
. . .
To start or hasten the animal, one kicks it in the flanks, or uses the long kaiila quirt.
Tribesmen of Gor Book 10 Page 56
I glanced to the large female slave, with the quirt, standing near the silver curtain.
Some patrons bring whips or quirts to the tavern. If they are not pleased, the girls are informed; a slave ring, with thongs, is fixed in the edge of every table; we strive to wait the tables well.
I saw quirts thrust in their hands.
"Kneel, Jason," said the Lady Gina.
In consternation I knelt.
The quirts were thrust to my face.
"Kiss the quirts," she said.
I did so, commanded by the woman whom I feared, who was my mistress.
The Lady Gina nodded to the girl Tela who then, crying out angrily, struck me twice with her quirt. Lola meanwhile broke her pose and looked at me, impassively.
I looked up at the Lady Gins. There were tears in my eyes, from the stinging of the blows of the quirt.
Both took their quirts well in hand. They were long quirts, some two feet in length. They held them now, each of them, with two hands.
I saw her hand reach for a quirt at the side of the saddle, but then she did not grasp it.
I knelt near the end of the line. The Mistress, with a long, tharlarion quirt, had begun her inspection.
"But, of course!" called the auctioneer. He hung the long, black kaiila quirt on his belt.
The auctioneer then removed the long, supple kaiila quirt from his belt. Twice he struck the girl across the back.
We saw the auctioneer remove the kaiila quirt from his belt.
I then lay back on my blankets, on the grass. I put my hands under the back of my head, on the folded saddle blanket beneath my head. The kaiila saddle and the kaiila quirt lay to one side.
"Perhaps it shall be the quirt," I said. "Perhaps I shall use the quirt on you, lengthily, as on a recalcitrant she-kaiila."
"Why is your kaiila quirt drawn?" she asked.
I lashed her once, savagely, with the quirt, between the neck and shoulder, on the left side. I did not see any point in wasting time with her. "Kneel," I said.
I held the quirt before her face. "You may kiss it," I told her, "or be beaten with it."
She kissed the quirt, the supple, slim leather.
At the flanks of some of the warriors' kaiila marched stripped white women, in beaded collars. Their wrists were tied behind them. About their throats, on thong loops, below the collars, dangling between their breasts, hung leather, braided kaiila quirts.
"Yes," said Cuwignaka. "I would like to own them. In my lodge I would have them naked and I would then, with my quirt, if necessary, teach them to obey me well."
"What of Bloketu and Iwoso?" I asked.
"If they were slaves," said Cuwignaka, "I would strip them and teach them, like the slaves they would then be, no different from others, to obey me well."
"Would you quirt them?" I asked.
"Of course," said Cuwignaka. "If they were even the least bit displeasing they, like the others, would be well quirted."
"Nonetheless," said Wasnapohdi, grunting, at her work, "do not be surprised if you find yourself well quirted."
"Canka would never do that to me," she said.
"Have you never brought him the quirt?" I asked.
"Once," she said, "the first evening in his lodge, he made me bring him the quirt, on my hands and knees, in my teeth."
"What do you suppose the meaning of that was?" I asked.
"That I was a slave, that I was subject to discipline," she said.
I had not been given a quirt, a permission quirt, beaded, such as might give a male slave power over such women. I looked at her. She was luscious. I could not so much as touch her.
I smiled. I saw that she did now wish to be quirted for insolence. A slave, of course, can be quirted for any reason, or for no reason.
I then, to her horror, strode to the side of the lodge and picked up the kaiila quirt which lay there.
"Please, no!" she said, frightened. "Do not whip me!"
But I laid the quirt to her well, five times, first striking her from her hands and knees to the robes, and then, as she twisted and rolled, helpless to avoid the blows, lashed her upon them.
"You wanted to be punished," I said.
"I did not want the punishment of the whip!" she wept.
"You will take what punishment your master decides to give you," I said.
In a moment she re-emerged from the lodge as she had entered it, crawling, with her head down. Grasped between her small, fine white teeth was the center of a heavy, braided, beaded-handled kaiila quirt.
I looked at the object. It was a heavy, supple, beaded kaiila quirt. It was a symbol, of course, more than anything else. It gave its bearer warrior rights to open slaves, those not housed in private lodges, for the duration of the festivals. It was good for all of the girl herds of the Kaiila.
"Disgusting! Disguisting!" cried the free woman, Boabissia, in her leather and furs, having returned to the fire, and she rushed forward, a stout, thick, short, supple, single-bladed quirtlike whip in her hand.
Some other men passed by me, going to one part of the line or another. Some of them carried leather quirts. Others carried whips.