I don't know that this necessarily applies to your CPL, because it probably varies quite a bit by brand, model, etc.
However, on at least one brand CPL and GND filter I have, inside the front ring, using the same threads you'd use to stack a second filter, there is a very slim retaining ring that unscrews out the front, letting the glass fall out once it's out. There may be a similar arrangement on the rear. Having never fully disassembled one, though, I'm not sure how to separate the front half from the back half. But, if you can get one glass surface out, you should be able to clean the hair out. Just be sure you pay attention to which surface of the glass pointed which direction.
It's quite possible, though, especially on cheaper models, that everything may just be cemented in, in which case things get quite a bit more difficult.
One other thing - you might take some shots of a clear sky at something like f/22 with the CPL on and see if you can even detect the hair in the resulting photo. Chances are extremely high that you can't. So, it's almost certain that you don't really need to do this - that hair bothers you a whole lot more than it's likely to bother the capabilities of your filter/lens/camera.