Sweating, hats and sunscreen will be a problem. Welcome to the life of everyone who lives in hot countries! But as far as using the regimen, it wont make much difference except for sweating. You may find that shirt collars may become bleached. You might also break out slightly more because of irritation from wearing a hat etc too.

But either way, I'm sure you will have a wonderful holiday - Egypt is an amazing place to visit.