If you have never watched the show survivorman I would suggest watching some of his stuff online, also look for Ray Mears.
You could probably make a good shelter without a tarp using pine boughs, (and a comfy bed) but at least bring a metal cup for boiling water, a fleece blanket, a good fire kit, and for a knife I would say try to get a hold of a one hand trekker swiss army knife, wal mart usually carries them. The saw is small but works amazing.
If you are doing a video though, I would do it in the style to show how having a bare bones kit can save your arse in the woods, anyone can find a bic lighter, (though I'd prefer to use a flint and good tinder) and birch bark is usually easy to find, my favourite natural tinder, it burns when wet due to lots of oils in it. (don't cut the bark off, it may kill the tree, peel old stuff from a big one or carefully peel outer layers off.)
Show how you can reflect heat into your shelter with large flat rocks, make tea from pine needles, try your hand at snaring squirrels, make a fish/frog spear, 4 days is a long time, you may as well do some stuff well you are there and make your video kick a$$!
Search for PSKits and you should get a wealth of info.