My chin is in a double Ferret Nation cage. It's a fantastic cage and she and I both love it...though I'm not sure it would help much with dust, as it's still a wire cage.
Are you leaving your chin's dust bath in the cage all the time? If so, you should take it out and only give him access to it for a few minutes once or twice a week. That's all they need, as too much access to dust can cause some health problems. Also, it massively cuts down on the amount of dust in and around the cage. I just put my chin's bath in her cage for a few minutes right before I clean it, and then all the dust gets cleaned up with everything else.
Also, are you using loose bedding, like aspen shavings? If so, you might consider switching to fleece liners and just giving him a litterbox with shavings to pee in. Wood shavings can be a bit dusty, so less shavings will mean less dust.
Here's my chin's cage so you can see what it looks like (it's an old picture, so the set-up is a little different now, but it's still the same cage):
but I do the dust bath in another smaller cage in another room.
(obviously the lid is removed when the chin is in there )
The glass jar for a dust house helps to contain the dust a bit, but the small cage also helps so I can have it in a different room that is easier to clean up, and it limits the amount of dust that goes back into the room with the cage. My chinchilla's cage is in my home office which has two computers so I need to limit the amount of dust in here as much as I can. Some people even put the dust bath in the bath tub so they can just rinse any excess dust down the drain after.
Another thing you can do is get an air purifier for the room with the chinchilla cage, that way any dust that does make it back to the room can, at least to some extent, get filtered out.