pine, aspen, or the like shavings are fine to use. Cedar is not. Never use cedar around your rabbits - not in bedding, not in pans and definitely not in nestboxes.
Sawdust is something you want to stay away from in nestboxes. The same goes for kitty litter, or those pellets that turn into sawdust when they get moist.
Personally, I only use shavings for a litter during very cold weather. Otherwise, I simply use some type of grass hay. The type doesn't really matter, but I prefer a long stem such as bluestem over orchard grass or bermuda. Just make sure it doesn't have any stickers or goatheads.
As far as the extra fur, I would never use anything that didn't come from the Mama rabbit. Luckily, Mama's fur gets very loose around kindling time and stays that way for a couple of weeks. If Mama doesn't pull enough, its easy enough to pull more from her from around her flanks. I've even pulled extra after 10 days to 2 weeks when the box needs cleaning. A bald Mama flank is a much better thing than cold babies.