Don't get me wrong, while I don't mind the idea of organics, I greatly prefer mechs, but this line of thinking is, and always has been ridiculous.
The hair and spinnerets on spiders are exactly where they need to be to be useful - they're on the best place, anatomically, for a spider to use and manipulate webbing. If we are to assume the spider-powers transfer to Peter in a logical sense, then spinnerets appearing on his wrists, and the "hairs" appearing on his finder tips and feet are exactly the best place, anatomically for them to appear in order to be useful. It takes far more of a leap in comic-book logic to assume that they would generate someplace UNuseful. His body would naturally adapt the powers of the spider to function properly for the biology and anatomy of a human.