That's a reasonable plan with a couple of glitches.

First, neither AA nor BA pay North American travel agents a commission. (BA pays ten bucks!) So you should expect to pay for the service.

Second, the traveler is at least nominally supposed to be present in Egypt to purchase the ticket. There are also now words in the rules file about having to pay for your ticket in the currency of the country of issue, or else it will be repriced to the higher value, i.e. the ex-USA price. I think it's pretty clear that OW is at least uncomfortable with what you propose.

I think the only thing that might work is finding an agent in Cairo that you're comfortable in working with directly. That may be as simple as getting the number of the American Express office there. Again, of course, unless BA is more generous to its TA's in Egypt, look for a service charge.