Apparently no one knows the answer to your question.
"The typical mesothelioma latency period is 20 to 50 years, with recent studies finding a median of 30 to 45 years. The shortest possible latency period is 10 to 15 years, while the longest is more than 50 years. Because of this long time span and because most people are exposed to asbestos as young adults or older, most of those who are diagnosed with mesothelioma and other asbestos-related disease are in their 60s or 70. Those diagnoses come after symptoms of the disease – a persistent cough or difficulty breathing – become nagging or debilitating."
The "good" news is that in the US in your 60s or 70s you only have about 15 years to live, anyway (depending on what mortality table you use).
You might be able to find a link correlating short exposure times (a few days in your example) to the likelihood of later mesothelioma.
The cell damage that asbestos does is on the molecular level and maybe someday they will have tests that can immediately determine this damage and its extent.