Repairing Wooden Chair Legs Scratched By a Cat?

How can I fix the legs on the chair that my cat has shredded without them looking tacky? It's the wooden legs of the chair. She sharpened her nails on them when we weren't around to stop her, and they're so shredded, they are like fibers. I'm not sure what kind of wood it is; either bamboo, or some type of softer wood. I really don't want to get rid of them, they kind of have sentimental meaning for me.

By Krista R. from Charleston, WV