Its safe. Even if you were to eat the feathers, its safe.
Permethrins break down (slowly) in sunlight. They break down rapidly via a carbohydrate reaction on the skin of all mammals - we are more dangerous to permethrin than permethrin is to us. (Except perhaps felines, who are lacking in an essential enzyme which catalyzes that reaction, so it occurs much more slowly on them). If we spray it all over ourselves (which we shouldn't do, because our skin destroys it), typically less than 2% of it is absorbed through the skin, absoprbed into the liver, rapidly broken down and excreted, with a half life under a day. That's why its typically applied to clothing, not persons.
More likely sources of permethrin ingestion come from veggies, where, relying on sunlight and crop dependent, it may be detected in trace amounts for between 30 and 90 days.
Via ingestion, a lack of symptoms is expected at rates of Permethrin consumption below 200 mg/kg - for a 165# person, that like drinking 0.5 oz of 100% permethrin. Or the equivalent of drinking 1/3 of one of those 16 oz bottles of Durvet 10% permethrin sprays. Honestly, the petroleum distilates init are mlikely far more dangerous than the permethrin. Temporary neurological sysmptoms are expected to be evidenced (nausea, dizziness, possibly tremors or twitching, headaches, etc) at doses 10x higher or more...
So, I think you are safe. But you can google permethrin oral dog toxicity if you want to read up on the studies, then do the same with rats. Humans haven't had a lot of oral studies done, you understand -but the link above has this gem from a dermal study:
Staff involved with bagging, mixing, or spraying a 5% preparation of permethrin (cis/trans ratio, 25:75) in Nigeria were evaluated with a questionnaire and urinalysis (Rishikesh et al., 1978). Regardless of the protective equipment worn by spraymen, only 2 mg of permethrin was absorbed after exposure to 6 kg of permethrin, which was excreted in 24 hr.
