It's an interesting question. There's no way the discovery of the Americas would be put off forever (some don't even think it would be put off for more than a decade). Personally, I find that mysticism played a large enough role in the daily lives of sailors that the disappearance of Columbus's fleet might spark some kind of supernatural fear that would at least stop Spain from arriving there in any hurry.
Regardless, the Portuguese would still land in Brazil soon after, and didn't Giovanni Caboto find Newfoundland before Columbus landed anyway? For these reasons it's only a matter of time before the Gulf of Mexico is discovered. By whom? Good question.
As far as my extremely limited knowledge knows, the most likely contenders (if not the Spanish, of course) are the English, Portuguese or Dutch. Imagine a Dutch Mexico, now there's a timeline. Though I'm probably wrong on that count.
Should the Portuguese arrive, the destruction of native culture in Mexico and the Caribbean might be greatly lessened. Disease would still be a problem, but the Portuguese preferred trade dominance over outright conquest and resettlement. What I know about the English colonialism in the era is that they preferred to steal land.