Just an observation: Remember that while Egypt is an Arabic and predominantly Islamic country, it is home to one of the oldest Christian sects (the Coptic church) so you'll definitely see many local women not wearing burkas or headscarves (though they are still very conservatively dressed). Just make sure your blouse or top is opaque ad not even slightly transparent.

As for crime, I'd say even low-level petty crime seems to be limited. The only way you're likely to be "robbed" as a tourist is to be (grossly) overcharged for goods and services.

There is apparently tolerance for non-traditional Islamic behaviour. I remember walking in some old Islamic (and very untouristed) quarter of Cairo last month and saw a young couple, the woman in a head scarf and burka, openly holding hands with her male partner. I looked hard and found no one staring or making comments. Everyone just went on with their own business. Sample of one but I was still surprised.