Why and how would they do that?
Venice had zero interest in the New World, in fact they'd pretty much be against any such things as it ruins the Eastern Trade which Venice was so dependent on meanwhile Genoa, on the other side of the Peninsula has the issue that it's to the East of the Strait of Gibraltar and thus any colonies it founded would be incredibly vulnerable both as a result of supply lines having to pass through the Western Med. and Gibraltar as well as the other powers deciding to just take them.
Venice OTL had no chance to make a move on the new world, because of the remarkable speed with which the Castilians took control of the Carribbean and Mexico. Since they had no territor, trading posts, or claims in the new world it wouldn't have made any sence at all for them to support it. If there is no conquista, and Portugal doesn't immediately colonize the same areas, then the Italian states, enamoured as they were with exploration, might be the first to discover Aztec gold, or the Carribbean islands incredible sugar growing capacity, and thus be the first ones to take an interest.
As for Gibralter, I've heard the arguements for it, and the idea that it makes colonization by a Mediterranean based naval power impossible is just wrong IMO. Genoa had colonies in the Black Sea without controling the Bosporus, and I imagine a similar arrangement could be made with Castile as was made with Byzantium. Yes, there is danger in falling out of the controllers good graces, but if you become fabulously wealthy you could certainly make it profitable to simply allow you through.
Pirates with bases or crew in/from the Maghreb are not the same thing as states with navies.
Pirates did establish bases in the New World, but they were also stamped out relatively quickly and were despised by pretty much all states.
The PoD here is going to be in the 1400s at latest, and at that time there was no universal hatred of north Africans, and in any event with an earlier PoD you can keep and strengthen the Maranids in Morocco to give you a good strong Kingdom with allot of atlantic coastland.
If the Portuguese think that the Western route will be shorter than around Africa they're not just gonna give-up because their's no shiny metal, yes without Europe thinking Central America was full of Gold colonization would be slower, but only by a few decades.
Aside from that, the lack of Iberian control itself makes it more likely one of the other Atlantic European powers will move-in, seeing it as prime territory.
The Portugese were never all that big on settler colonies, and an American colony that doesn't come close to equalling their rout around the cape of good hope on an annual basis will find little support. As for them believing that the western rout is faster, there is a reason that the Portugese didn't hire Columbus. They'd done the math, and Columbus estimates about the size of the world were totally off in their opinion, and a giant landmass with scant valuables (to their knowledge) and no way around just makes it worse.
And the other Atlantic european powers, France was strongly attatched to its continental ambitions, and had very little navy at the time of the conquista, while England in this period was experiencing weak rulers and the Wars of the Roses, in addition to strong rivalry with France and little real control of Ireland and Scotland. Who else is there?