I think you are panicking for nothing NC . I have been using the same Sawyers .05 unscented mix for at least 15 years. Been spraying it on any clothes I use to go in the woods for summer checking cameras and cutting up fire pit wood, hunting in the fall, and and a very light spray for winter. I have no concerns.
I spray it both in and out . For summer I wear a very thin coverall with a pair of jeans shorts and a tee shirt underneath. So the coverall is rubbing on my skin. Never a tick bite , No rashes of any kind , or any other issue . I actually put a heavy spray on that coverall and let it totally dry for a day. I know tons of people doing the same for hiking , checking cams , and camping . Never heard of any issues from anybody . The campers I know not only spray their clothes , they spray the inside of their sleeping bags . No concerns or ill effects from anyone. And its been years they have been doing this. A couple guys I know actually wipe a very light diluted mix on their dogs . No issues there either. But dont spray anywhere near a cat where they can get it on them while its wet. They could get sick from it. Its fine after its dry. I actually have sprayed our cats bed and dried it . Found dead ticks in there from them dragging them in when they go outside. Never affected any of the cats at all . Once the spray is dry , everything is good to go .
One last thing . I spoke to the company a while back. One of their biggest clients is the military. Permethrin works on all kinds of critters. Sand fleas in the middle east , and all kinds of swamp bugs in the jungles. Do you think for one second they would let our soldiers use that stuff if they knew it was harmful to them ?