I've used wigs in other cosplays; I generally use wigs for short-haired characters and my own hair for long-haired characters, since long wigs tangle excessively and are quite expensive. On the other hand, non-permanent hair dye rarely looks good, or at least authentic. Since Kat is kind of cartoony anyway, I went with spray, but it never looks quite as professional, and it rubs off on /everything/.
Basically, pick your inconvenience.