I went there about twelve or thirteen years ago and it was perfectly safe. That was before a lot of anti-Western sentiment started escalating in the Middle East though (before the Gulf War, before the first suicide bombings started, etc.) It was perfectly safe, we saw the pyramids, Cairo, pretty much every tourist destination there was. It was a fantastic experience, I couldn't recommend it highly enough.
I don't know if you could see enough in only a few days though. I'm 99 per cent sure you could get there, and get around on tours or personal guides (they see you're a tourist and offer you anything, you don't have to hunt for tour guides, they find you, but you have to be careful and make sure they're honest). That said, as fun and exciting as it sounds, going overseas without an infallable plan is probably the worst thing you can do and will only get you into trouble, so I'd say you're better to be safe than sorry, and have a solid itinerary, plan, budget, etc.
I'm sure others here have some more specific advice, since it's been years since I've really travelled overseas, but I hope I've been of some help
