If you just have a ready to use spray container instead of concentrate, you won't be able to make a dipping solution. I imagine permethrin comes in a concentrate to mix up large amounts to spray down a coop, for example.
I use Elector PSP (spinosad) and it's a concentrate. I mix a dipping solution and soak the chickens legs and feet in it. One soak and the mites are gone for good.
But soaking in warm water and then spraying with your permethrin, followed by a thick coating of Vaseline or castor oil after the legs are good and dry will work, too. The oil seems messy, but it eventually all wears off and the legs are clean again, minus the leg mites.