Permethrin IS permethrin. There are two grades, pharmaceutical and technical. The pharmaceutical has higher purity and is used for topical treatment of scabies, and head lice, etc. The technical grade is lower purity (about 94%), which is what is used for the animal sprays and is what I used for treating my clothing. Once it has dried, the clothing is not toxic or irritating to humans.
While it is a neurotoxin, it is inactivated by the skin and the EPA does not classify it as a carcinogen.
It does have a strong odor when first applied, but it dissipates (I don't know about deer, however).
As far as spraying a mattress, it is commonly used for treating for bed bugs.