Third party wiring internet into asbestos home

Hi all, we are getting the internet wired into the house tomorrow, and the providers are using third party. We don't have a choice in who. Now I am ripping my hair out to trying to figure out what is acceptable practice for drilling into asbestos walls - especially into bedrooms. Apparently it'll be few small holes through the wall, where the wire will run.

Does anyone know what I should accept from the worker? I worry that 3 teeth Sam is going to show up with his Ozito power drill and go nuts. What saftey measures would you demand? We've had one worker who was gong ho about it, and I don't want that again.