Cotton candy? Thats the only thing I can think of.....
Ive never tried it, so I'm not sure. I wonder if you just make it thicker than you want to make up for what melts, and apply with a tiny amount of piping gel, if that would work?
cotton candy does melt after added to frosting...did that over Christmas with a gingerbread house.
If you wanted to use regular frosting you can just use a simple knife technique...spread on your frosting and then with the knife parallel to where you're working you lay the knife onto the frosting and pull up or sideways. i actually have a cat cake that i did this to in my photos. OR you can mix multiple colors of the cat together in one bag, pipe them onto the cake and spread them around messily to look like fur.
i went through all that and don't know where or how you want it to look like fur 
lol
The cat is going to be sitting up and so the whole thing needs to be covered and furry. Do you think I would be best to pipe first then mess it up a bit after? I want it to look good and not a shabby mess, dont want to spoil her birthday!
Many thanks
Em
Your question reminded me of this picture I saw last halloween- it's a scary clown pic, but the hair is made of homemade cotton candy- looks so real! Maybe you can contact the maker??
http://cakecentral.com/gallery/2189205/2011-it-cake
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