Judging from takahirokumiko and zirconmermaid's comment, it seems that you should avoid saran wrap completely if you're putting something in the oven.
I was also typing up quite a bit, but zirconmermaid already beat me to it so I won't write any repeats.
Lessie... Yes, an X-acto knife should be enough to cut through baked polymer clay. I've never tried to cut something as big as a doll's head before, but if it cuts polymer canes then I'm pretty sure it can cut through what you're planning to make. I also think a wooden core will probably be more stable and easy to use, but I've baked plenty of polymer clay miniatures on top of aluminum foil without it sticking or anything so it should be fine.
Also, remember to get a mask to wear when sanding it. I think people tend to skimp on this because they're too lazy to go and buy it/think it'll be fine without it, but
anything that is sanded down will produce tiny particles of dust that will build up in your lungs. Besides, in the world of BJDs there's already so many uses for the mask that you might as well get one (e.g. face ups, modding resin dolls, removing seams, making doll parts).
Is there any particular reason you're using polymer clay to make the doll? I just did a quick search on google and it doesn't seem like the recommended material for it.