Basically, no, in my opinion. Putting your degree choice at the whim of one university really isn't a good idea. You can't just play dice with your life - Engineering and Egyptology are too different for that. I just find it hard to understand how you've got to the position where you're willing to put your choice of degree, which could well define the course of your life, into the hands of chance.
You've still got time. Carry on doing research and find out as much as possible about future career paths as possible. I know it's easier said than done but I can't see your plan above ending well.
You should re-think your plans in case what you want does not work out. It is always good to have backups.
Pursue your interests. I had an expectation to do Medicine for a little bit, and Law for a couple of years too - because my family would be proud. But in the end I applied for Economics because that's where my heart rests. I didn't realise this until I sat down one day and scrolled through every course available at the universities I would every consider (I suggest scrolling through Manchester's online prospectus simply because they offer most courses). Eventually, after looking at the modules, you'll discover your greatest interest.
You're clearly undecided as those two courses are very different. Perhaps there's a bridge between them that you'll discover through research.
As someone previously mentioned, do something you are truly interested in. You may change your mind so many times. For example I started sixth form with the intention to do law, I changed my mind so many times. It went from law to law and French, to law and German, to French and German to French and Japanese to Japanese and Russian to Japanese and German to French and Spanish to French, German and Spanish. I actually applied for Mandarin and French in the end. My point is you do not have to decide now. Explore a range of subjects and courses and pick the subject that you want to study and a subject that excites you, after-all you're going to study it for at least three years.
I would advise STEM but if you don't apply for a STEM course I would suggest languages (very biased), economics (if you don't consider it a science) or law.
So basically you would only consider studying Egyptology at Cambridge and if that wasn't an option, you would study a completely different subject? You can't be very committed to Egyptology if that is your plan and Cambridge will likely pick up on that in your interview and reject you - so no, not a great of plan. FYI Cambridge isn't the only good university which offers Egyptology, UCL's Institute of Archaeology is definitely equal to Oxbridge in terms of academics, research and subject prestige.
Your pathway into a good job is probably going to be easier with an Engineering degree but that is not to say you wouldn't get a good job with an arts-based degree. Do some LinkedIn stalking and find out where people who study Egyptology/similar subjects end up. Do you actually want to be an engineer or is it just the money that interests you?