I also have really thin hair, and would be quite upset, since there is none to spare. My current job required a drug test but it was a swab inside your cheek and then hermetically sealed (sure...) and placed in envelope to be mailed to the lab.
There was a urine test for the previous job. If you've had to do this, it's an experience. The door to the restroom outside the nurse's station is left ajar to insure you don't alter the sample.
Then they called, and I had to have it redone. They said I drink too much water. I had to cut back on the h2o and visit them again!!!
Since I've never done drugs I wasn't concerned. Obviously this is a test I passed !