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Paper Mache Clay
Thats optional. The baby oil/mineral oil is just to soften it a bit and make it more malleable. But not neccessary to add.
You can dip your finger in a bit of water and rub over the surface to smooth it a bit. Don't dunk the whole thing in water though... just rub it with your wet finger. :)
No cos it'll become less clay like, and become more like sticky putty. It'll be a mess!