The answer is...

...St. Blaise is the patron saint of both wool-combers and throats because of his specialty in miracles, and how he was martyred:

The miracles St. Blaise is credited with performing all have to do with the healing of afflictions of the throat (choking on fish bones in particular). Why he chose the healing of afflictions of the throat as his category of healing, I don't know. I suppose in the days before the Heimlich maneuver it was a very useful thing indeed, as well pre-antibiotic strep throat issues. Everyone's got their talent, and St. Blaise's was throats.

As for wool-combers...St. Blaise was martyred by being hacked to death with iron combs in 316, a favorite instrument of torture of the time. He was also beheaded for good measure. Apparently those combs resemble traditional wool combs, and thus St. Blaise was adopted by professional wool combers as their patron saint, and eventually he became a symbol of the wool trade in general. Although I was raised thinking St. Blaise's Day was February 2, some sources say it's February 3.

If you've ever used "modern" wool combs, I think you would agree that things haven't changed much. As a tool of self-defense, as long as I could keep my grip on my double-row combs, I could inflict serious damage on someone with minimal effort if need be. Raking your arm with carders is no fun; puncturing yourself with wool combs is a tetanus shot at the very least and considerable blood loss if you hit your thigh (which is a possibility, given the swinging motion used during combing). And there are combs with several more rows of teeth. Armed with those and a blending hackle, who would mess with you? (Assuming anyone would get close enough to the weirdo swinging pointy metal objects with a gleam in her eye....)