I vote for having a man with you over wearing a veil. The previous is a greater guarantee of protection as women with hijabs still get harassed. Just dressing modestly does wonders, too.
I also vote for "stone cold icy death".
Language is also a great tool for your safety. Brava for learning some Arabic before you get there! That way you can TELL men you're not a whore instead of pretending to be part of some religion that you're not (I'm assuming, forgive me if I assumed wrong). Tourists in hijabs get "discounts" (not even Egyptians get discounts, really) because vendors think they're Muslim. When vendors find out they've been had by a woman who would never think of converting, it's not a good situation.
Keep in mind that threats against tourists are not taken lightly. You can report anything to the police, even incidents of other policemen harassing you. Female tourists seem to enjoy more protection than the native women, unfortunately. I wouldn't go around à la egyptienne.
No one is exaggerating about the traffic. Be very very careful. Many Egpytian drivers don't use their headlights because "it's rude to the other drivers". Traffic signals are for decoration. Pedestrian accidents are very common, so pleeeease be careful!
I would definitely explore teaching English. I only have a basic TESOL certificate and less than a year of experience teaching, and I was offered a job at a British school during my short visit (I don't know WHAT they were thinking, but I'm just offering some encouragement!) I would even suggest taking a short visit for some reconnaissance/job hunting. That way, you could find out about how to get contacts for tutoring gigs, too.
Good luck! Have fun in Oum el Dounia!