Wumps Wady?
Not exactly sure how well it would work unless going off a canon that Fluffies do not mutate and are all one standard size after reaching adulthood. It would require fairly precise equipment and highly complex scanners otherwise, as well as a steady supply of obsidian scalpels unless going for the “Fluffies are immune to disease and infection, and heal magically with medical gel”. It might work by locking them in place and letting them feed as they’re operated on, though I doubt anesthesia would be offered plus they could pass out in their meal and die and/or be violently raped or beaten to death while locked in unless the machine covered them in a lid like a bread box, though they might equate it to a Sorry Box. Unless going by the concept that spaghetti is overwhelming against all other thought, I would assume the few takers are unlikely to be breeding anyway. If anything it would have to be a trick, again requiring canon where they do not pass knowledge onto each other, have poor memories, or just disbelieve everything they are told.
Interesting parallel to the men who volunteered for castration in Europe, the Middle East, and China though.
I’m really not sure how you would do it for females. The fetish art of monkeeman0918 comes to mind.
Warning on the image and link: not for the faint of taint.
I guess you could use radiation or something, assuming there isn’t some kind of cutting tool going into the cooch or some kind of needle that expands into a blade severing the fallopian tubes or something. Plus, suppose the machine has no way to differentiate a female getting into a neutering machine. Does it infibulate her? Most artists and writers don’t even give females a sex drive, meaning it does nothing except make intercourse painful for a little while which most stories would not be affected by since its already either painful for females or Fluffies reproduce by rape or forced breeding.
Given its Fluffies you could go a more Hugboxy route. Going with my idea of the use of licorice asbirth control, implant something or justinject something, maybe use a needle to the brain or insertion of a brain bulb/programming chip, to nullify their sex hormones without literally nullifying them.
The more Abuse route might be to remove the skin on the penis as well as the entire cocksheath, maybe add a slight clamp or even some kind of electric shock delivering device to the vas deferens which would make sex and orgasms excruciating. Maybe severely reduce the depth of the vagina so all penetration results in touching the cervix, which despite what porn leads you to believe hurts like a MOTHERFUCKER. Maybe eliminate the Bartholin’s gland, though Fluffy sex portrayals suggest its not going to change much. Maybe some kind of permanent severe vaginismus.