To contain a cat, I would wrap the cat in a towel. That was for nail clipping, though.
When our cat got mats, I came at it like I did my own hair (which could start to go to dreadlocks in days, when it's long)...just kept brushing tiny little strokes, going further and further into the mat. I think I remember vaguely just using the very end of scissors to just get into the mat a tiny little way...that would actually get me pretty far, because mats, like (my cousin's) dreadlocks, build on themselves, and if you cut them just a bit, it can all unravel (which is why my car looked like a blonde cat exploded when my cousin cut her dreadlocks shorter on her own...they just started to unravel). Then I would just brush and brush and brush some more until it had worked its way out.
This was NOT a one-shot thing. But I suffered along with her when we had to contain her...cat dander was bad enough for me. But *stressed* cat dander was dangerous for my lungs, so I tried to avoid stressing her as much as possible.
Good luck!