In the US, if I’m remembering right, women are just advised to avoid soft cheeses in general. Along with deli meats, and a bunch of other things. Although in the US you can’t have raw milk soft cheeses to begin with.
There are definitely people for whom the cheesemaking process alone is an insufficient safeguard. But for the general public it’s not something that super matters.
Cheese as a method to make milk safe to consume predates pasteurization. It’s not the same risk profile as unpasteurized milk.
There’s a solid chance you’ve eaten cheese make with unpasteurized milk and not known it. As far as I’m aware, there aren’t labeling requirements around it in the US or Europe. Whether or not that’s sensible, I don’t know, but it might give you a better idea of how dangerous governments think this cheese is.
This is currently phrased more like a joke than a riddle. It does work as a joke.
Maybe try looking up paw more generally. Merriam Webster seems to think it can be used to describe any animal foot, or human hands (albeit with some baggage), or as a verb for rough contact.
For further uses outside of explicitly furry animal feet, a few more come to mind: southpaw, (left handed baseball player), catspaw (knot/hammer/chuck), and chicken paw (chicken foot, usually in the context of food).
In terms of the specific expression you’re asking about, it’s from a work of fiction. If evocative language serves your story better, even if it doesn’t fit as well by literal meaning, that’s reason enough to use it. In this story paw may have better communicated crudeness than hand would’ve. Or maybe the author thought paw better drew out the parallels with a lucky rabbit’s foot. Ultimately, why it was chosen doesn’t really matter, the imagery was powerful enough that we’re still talking about the story.