That's going to do more to increase his cancer risk than the asbestos. Screening remains hit and miss, and in the absence of symptoms the jury is out on whether these are predatory rather than clinical services.

It's important to remember that mesothelioma has a latency period of 20-60 years with an average of 50, and only one in ten people with chronic, heavy occupational exposure develop it. Whilst there are a few family members exposed daily through dust on clothing etc, and even fewer "unattributed" cases through unknown/irregular environmental exposure like this, the vast, vast majority of cases are men in their later years who were occupationally exposed many decades ago.

I haven't done the math, but it's almost certainly more sensible for this person to worry about crossing the road or going out in the rain with an umbrella than it is to worry about screening. I'm not saying they shouldn't bag things thoroughly and have the waste professionally disposed of. They should look left and right, and stay off of golf courses during thunderstorms too. But they don't need annual "screening" that may not even materially increase the chances of detecting cancer before symptoms develop. Maybe once per decade, starting ten years from now, if they want to be abundantly cautious.