About 25 years ago, all sorts of Rube Goldberg devices were sold to shops to supposedly minimize exposure to asbestos dust during brake work. The term "Tempest in a Teacup" comes to mind, unless somebody is going to make a living restoring these old brake systems 8-10 hours a day, every day. Simply wetting down the brake parts with a mist of water will drastically reduce any exposure to airborne dust, and whatever minimal exposure you happen to get will be far below any threshold of danger I can imagine. Once the brake system is cleaned up once, the risk is pretty much nonexistent once the newer style brakes with minimal asbestos content are installed. Don't get stupid, but be aware that most of the risk hype is way exaggerated.
It was amazing just how panicky people got about disposal of vacuum cleaner bags and wash water or solvent once the residue was captured. You'd think we were handling nuclear waste or something! A lot of people made a lot of money setting up hazardous waste disposal schemes and trying to convince shops to buy their services!
Jerry