Do I need to remove cap nails before re-roofing?
That's between you and your roofing manufacturer. The new underlayment may be more likely to wear through on the protruding caps, nuking your warranty. (Plastic caps are always protruding somewhat.) 

I'd hire a couple teenagers to pull them. With a cat's paw nail puller it shouldn't take long. Many re-roof jobs I've done have required several thousand roofing nails being pulled individually as well.