What a fascinating idea!
The idea of a shared or coordinated space flight with Khrushchev's Soviet Union is a fascinating idea. The idea has a lot of appeal--both from an optics perspective, and from a practical standpoint. If there can be peace between nuclear powers, what better way to show trust than in a place with no borders to infringe on?
A part of the feasibility of this shared initiative, would be, I believe, the unique place that space holds in the collective imagination of mankind. It is a place with limitless possibilities--from utopians to Posadists and labor unions on Mars popularized by Joe Hill during the 1930s. (Tangent: there is a wonderful paper on the imaginative pull of space for social engineering found
HERE that lays it out quite well). Space, in other words, especially at the time, was viewed as a limitless frontier.
Now, let us imagine what a successful joint mission between the Americans under Kennedy and Khrushchev might reap. Let's for the sake of argument, say that the two great powers collaborate on putting a living creature on the moon. The United States managed it in 1969--with doubled resources and coordination, let's be optimists and say that cuts a manned moon-landing time in half--say 1966 instead of 1969. But up to then, there are bi-annual or annual combined missions between the USSR and USA exclusively in space. This help normalize relations--make this less of a one-time team up, and more the norm when it comes to space.
Lets dream big and say that the initial cooperation works with satellites--and proves successful enough to warrant a manned mission to the moon. Americans and Soviets both.
This kind of big-science and propaganda could keep Khrushchev in power past his 1964 deposal date, by Brezhnev and the KGB. Kennedy was similarly uneasy with the seemingly free rein the CIA had in American policy, saying on several occasion he wanted the agency brought down to size and under control. The conservatives and reactionaries of America would doubtless hammer the Kennedy--who likely would have won a second term in this reality--for being 'soft on the Commies.' But not all of America is conservative, and any reason to step away from nuclear armageddon would be welcomed. Kennedy would be able to slowly draw the teeth of the military industrial complex, if the shared theater of space becomes more accepted as a concept.
If there is finally a sphere where peace is the base state rather than the exception, that could change everything.
On the Soviet-side, a limited partnership--with good results--would allow Khrushchev a way to pivot from some of his less successful policies--like trying to plant corn everywhere, even in places that weren't suited for it, and give him another cudgel to bludgeon Stalin's legacy with. It would provide him with cover against the hard-right factions of the Soviet government. With Khrushchev in power longer, with more international and political capital to spend on de-Stalinization, it is possible that the Khrushchev thaw would have time to recover from its early domestic blunders and bolster its image. The KGB's reach and teeth blunted, diminished. The regime that crushed the Hungarian revolt on 1956 could rehabilitate its international image as a country focused on progress. By focusing on the space race, Khrushchev could possibly de-escalate nuclear production--and do it under the guise of international cooperation, to show the world the USSR wanted peace.
Maybe we get a world without a Vietnam. Without escalation. We see an explosion of investment in space-tech, and far less in the creation of a cultural panopticon.
Perhaps the wall comes down in the seventies, rather than the late eighties.
What do you guys think? I'm just spit-balling here.