Thank you all for the responses. Yes, I am going to be checking baggage. I've talked to BA about the ability to interline the baggage all the way to CAI if I booked the RJ flight, but they wouldn't confirm that they could over the phone and it was something to check with the counter agent about. With the recent change to the OW policy on interlining, it makes me a little nervous.
I'm still contemplating whether I should take the risk, and it definitely is a fairly big risk, of the close connection. But it's now 28 hours until my first flight departs and I'm running out of time. I had my heart set on seeing the pyramids, but maybe the world is trying to tell me to wait. Other second destinations that all could work are BUD, IST, and ATH.