How can I prevent wood shavings from getting stuck inside one of my guinea pigs?

Yeah, I really don't like wood-chip bedding. The best thing to get is a paper bedding, like Carefresh (thats what I have recently switched to,) because the oils in wooden bedding are not good for guinea pig's skin and obviously, from what you said, not good for their overall health. Plus, using a non-wood bedding eliminates odors better and absorbs a lot more, so you actually come out saving.