I give corks (which have never been used for food, I don't know if the residue would be a good thing) to my cats to play with. My ratties LOVE finding them around the house, and leave little piles of cork everywhere. They don't seem to try to ingest any of it, so I always assumed it was safe, but I could be wrong.
My mom is a wine fanatic so we constantly have a supply of corks. I don't think too much wine gets soaked into the cork(someone please correct me if I'm wrong), but I still let them sit for a while then I rub a yoggie on it or let it sit in the yoggies for a week or so and they go NUTS.