If Columbus had sunk along with his ships, the Catholic Monarchs would just shrug. They'd have to listen to some reprimands from their advisors for committing money and resources to such foolish endeavour. The monarchs themselves never had much faith in anything substantial coming out of Columbus voyage.
A handful of years later, some Portuguese navigator would end up discovering Brazil on the outward journey to go through the Cape of Good Hope. The main difference would be that since Columbus never got to the New World and never made some colonies in the Caribbean (Which were legally Portuguese due to the Treaty of Alcaçovas, which granted everything below the Canaries to Portugal), there would be no need to sign the Treaty of Tordesillas. It is most probable that the Portuguese were already aware of the American continent (Or rather, that land existed at some point in the Western side of the Atlantic, that due to Erastothenes calculations, couldn't be Asia but was actually an uncharted land.) before Columbus set out to discover "India" for Spain.
But, if Columbus sunk down with his expedition, the most probable course of action for the Portuguese monarch at the time (John II), was to publicly continue with the expeditions along the African coast while secretly charting the American coast (Which mirrors much of what it was the original secrecy policy of Portuguese discoveries beyond the Canary islands).
Considering the manpower of Portugal, in comparison with potential competitors that had far more manpower and/or resources to commit to such adventures (Spain, France, England, Scotland, the German Hansa), it would be a much more sensible decision to keep a new continent in the dark for as long as possible, so that Portugal would be in a much better position of strength once the knowledge of the continent would become public.
So if Columbus died, the continent would remain publicly undiscovered. Portugal would probably continue secretly scouting the American coasts until either:
- Any reputable captain (vulgar sailors accounts of new lands, natives and animals across the ocean wouldn't probably carry much weight) that had knowledge on it would publicly spill the beans to another country's court, in an attempt to gain favours or rank that couldn't be gained in the Portuguese court (Like Magellan did).
- A decision of the Portuguese monarch to make the discoveries public (Possibly if the Portuguese government wanted to start a colonization of the New World, which would involve recruiting thousands of people to move there, hence nullifying any possibility of remaining a secret).
- Some other navigator, either successfully convincing a foreign court to pay for the costs of outfitting an expedition in the country's name to find some fabled lands in the West (Like Columbus did), or being wealthy and with enough contacts to privately outfit such an expedition, requiring the good will of an Atlantic nation (And Portugal, if knowing the purpose of the expedition, would never allow the ships to dock or resupply there) to serve as launching ground (Quite a lunatic idea, which requires good faith and capital of a great many people, and skills in navigation and crew to successfully accomplish it).
Also, Due to the way wind patterns and water currents happen in the North Atlantic, the only reasonable chance of any knowledgeable private expedition suceeding would be if they set sail from Portugal/Spain, onwards to the West (Like Columbus did) or using the Northern currents North of the British isles, that leads to Iceland, Greenland and then America (Like Leif Ericson did), because of the latitudes between Denmark and France, the wind and water paterns go from America to Europe.
