How could Ottomans fail to conquer Egypt?
Giving their clear strategical superiority in early XVIth century, I suppose that it means we may need an earlier PoD but it would be best IMO if we consider one that take place after the conquest of Constantinople.
I think we may have some possibilites, ranging from a possible Ottoman dynastical instability, stronger Savafids, and (while I'm not sure how too) Mameluks undergoing a quick reform.
Everything goes as long as Egypt remains outside the Ottoman Empire (Holy Places are free for the taking however), and you don't have to preserve Mameluk rule.
What would happened from there? It seems that decline of Egypt was more or less not quickly recoverable with the spice trade being hijacked by Portuguese, but was it this of a doom for whoever would rule from Egypt?