Genoa was a large trading power *in the Atlantic* during the pre-game period, though, historically; Columbus is thought to have travelled as far as Iceland. So I think it's certainly possible that if they were in a position to finance the expeditions, and the Italian explorer guys had not hired themselves out to the four main Western European powers (which in Aberration do not exist), Genoa could have become a colonial power.
As far as the physical size of the strait, it is about one-third to half the width of the narrowest portion of the English Channel - narrow enough that one shore can be seen from the other, but wide enough that it could not be closed by the placement of fortresses on either side and creating a cannon crossfire (at least not until post-Napoleonic times).
I don't believe there is a game-mechanics way to close the strait completely, anyway; they could certainly have a fleet based there, but it would only stop another country's ships if they are at war. Is there a way to encourage the AI to so place its ships, though? That might be realistic...
Imposing tolls however - possibly in the form of creating a COT, boosting local tax base values, or both - seems rather do-able and reasonable.