I don't think I'd feel comfortable going out and galavanting around Egypt without some form of tour group. And while it's a bit eery having armed security around, it also gives and odd feeling of safety.
This part of the world is much to amazing to pass up a visit because of those types of fears.
Any big city can be dangerous, if you're not aware of your surroundings... Cairo, Rome, Barcelona, New York, etc.
I did see some private tour buses at the port, but I haven't talked to anyone who arranged one. We normally do that in many ports of call (have pre-arranged that for Turkey), but thought in Egypt we'd do the ship's tours.
I actually think the cruise lines should offer more of the smaller van tours as options for ship's excursions.