It would have appeared a weakness for the US to admit that the Soviets had emplaced missile installations in Cuba, especially after the failure of the Bay of Pigs invasion the previous year. On the other hand, it would have appeared to bolster the alleged (and false) “missile gap” that Kennedy had campaigned to the Presidency upon. It would have widely been seen in the US as a provocative move by the Soviet Union, although as you point out the US already had the intermediate range PGM-19 ‘Jupiter’ missiles in Turkey and Italy, as well as PGM-17 ‘Thor’ missiles in the United Kingdom, all of which could reach Moscow in twenty to thirty minutes.
Given that the Soviet missiles were of poor accuracy and even worse reliability, it seems probable that the Soviets would have been willing to trade retracting the missiles in exchange for the US removing IRBMs from Western and Southern Europe, which is what we were planning to do any as the first LGM-30A ‘Minuteman I’ wings were fully deployed. Although I’ve never seen any confirmation of the following hypothesis, I have the suspicion that this exchange may have been the primary objective of putting missiles of questionable operational status in Cuba and allowing such information to be leaked through Penkovsky whom the Soviets already knew to be an agent providing information to American and British intelligence services. (According to Peter Wright, there is good reason to believe that Penkovsky may have actually been a double agent, but even if he was not he could have been used to send false intelligence to the the CIA and MI-6.)
In the case of the scenario proposed by the o.p., Khrushchev may have appeared stronger and held his position as General Secretary and Chairman/Premier longer, but given the unpopularity of his attempted economic reforms in the Politburo and the alignment of factions against him, it likely still would have been deposed sometime in the mid-'Sixties by the Brezhnev faction with Kosygin or some other functionary as Premier. So, I wouldn’t expect major alterations to history. However, the negotiations to remove missiles from Cuba and Europe might have been public accord rather than the secret negotiations which transpired, and could have potentially lead to more interchanges that could have reduced tensions and alienated some of the needless brinksmanship in the strategic arms race. The various proxy wars through client states in Southeast Asia, the Middle East, Central America, and Africa, however, seems an inevitable consequence of the two nations facing off.