Did a wee bit more research for you, im not a spider fan *AT ALL LOL*
but this particular species is a form of Hogna basing on its eye configuration, but it is indeed, without a single doubt in my mind a wolf spider, and i do agree with swords, nono on the cotton ball or any form of tissue paper or cotton, just a shallow water dish with a slight incline for it to reach its head in safely is all you need, these spiders are VERY fast in my experience with them around the house here so be careful when you reach into that cage to take that out lol.
Swords - most wolf spiders are pretty aggressive when confronted, and the ones here reach about the size of a silver dollar piece, sometimes a tad bigger.