Where did you get this idea from? Why did trade decline through Egypt?
Trade declined through Egypt because of the discovery of routes around Africa that allowed European powers to circumvent the Mideast entirely. This affected Venice severely because their predominant trading thrust was from the Mideast to Europe, and was IMO one of the main reasons of its power decline relative to the rest of Europe.
If Venice controlled Egypt, they could logically at least mitigate the detrimental effects of African-rounding competitors; this is all very hypothetical, but a Venice that set up shop in the Red Sea could try and force, say, the Portuguese out of the region in the same way that the Mamluks attempted to.
The suggestion for including the Straits of Gibraltar as well is to open up the Atlantic for Venice as well in the age of the lucrative New World trade, the same concept behind its current UHV3.