You guys need to get on top of dealing with the dust, don't just put up with it or use harder methods because the way easier ones might create it.
Toolstation sell huge rolls of polyethylene sheet (it's about as thick as the bags your gf / wife / mum puts your butties in
). It's DIRT cheap.
Buy a roll, chop off a length and then strategically tape it over the doors / passageways / walls to stop the dust getting into the rest of the house. Drape it over anything that will take ages to clean it back off (intricate surfaces) or that it'll scratch if abraded at all (finished wood). Let it settle, hoover it up. You can tape massive 'bubbles' to the reverse side of the problem (making sure tools going through can't catch on the other side).
If you're going to be using diamond tools or hammer drills, get yerself a half mask respirator and some P cartridges. Should have one of those handy anyway really if you're using abrasive tools often.
But in terms of this specific problem, it depends a lot on what they're built the wall out of. Make some inspection holes and report back. Make two or three (particularly if the house is old). In ours, for example, I just took a stud wall apart with the bottom half being solid clay brick and the top empty stud cavity - the brick at the bottom was the olden days backing for half way up tiled walls I think (no plasterboard), might also have been to fix the toilet / basin / bath etc.
It may just need something unscrewing or taking apart by hand. The saw method is good, and the chisel (you can use a chisel bit in a roto-stop hammer drill if you've got one or can get one from a friend). And the unblocking method.
If it's just a stud wall, take your shirt off, oil yourself up and run through it like Van Dan does in Universal Solider.
Always isolate the mains before running through stud walls. Live gas and water makes it look cooler, particularly if you're smoking a Marlboro as you go through.
