Not sure if it would be "healthy" to try to sideline Stalin...
The man was in awful health by 1953, pushing him to nearly a decade more of life might work but he's just not going to have the mental faculties to do what he once did.
It should be noted that the post-WWII Soviet Union was a very different place than the absolute power and one-man rule that Stalin had consolidated in the 1930's. During the war, Stalin for obvious reasons could not engage in the periodic cycles of purges that he did to clear out old-guard officials and elevate people loyal to him. Stalin did this kind of thing in a cyclical way: he initiated a purge to get rid of people who were either too comfortably entrenched in power or actively opposed to him and then usually culminated it by disposing of the head of the secret police and thus decapitating the most crucial figure to the operation of the Stalinist state (who could very easily build his own power if left unchecked), Stalin likely had plans like this in place for Beria (who was deeply unpopular and had literally no power base without Stalin and was historically ousted and executed shortly after Stalin's death).
Stalin because of the war, however, could not purge the party or the military (he did quietly reassign Georgy Zhukov who he thought was a threat to his power) and this was almost assuredly the ultimate purpose of the Doctor's Plot: to reveal yet another conspiracy-in-the-making against the Soviet government and purge anyone who opposed him as well as clear out old-guard officials like Molotov to make way for a new generation of Soviet leaders.
While he will likely be able to carry out the Doctor's Plot and purge the party in his early years, his mental decline was becoming fairly pronounced by that point and I don't think he would have lasted until the 60's. If he lived on to the 60's, sooner or later, the task of actually ruling the Soviet Union is going to default to Stalin's inner circle, probably much like OTL: figures from the inner circle such as Malenkov, Molotov, and Beria will serve as a collective leadership to keep the nation stable and also to prevent any one man from doing what Stalin once did and building an autocracy centered solely around himself. Stalin really won't have a say in this: he'll be fighting to maintain mental cohesion and prevent urinary incontinence, he won't be able to rule the country.
Needless to say, again like OTL, Beria is likely going to get ousted and purged himself. Even if Stalin is still alive, Beria is too dangerous to be kept around and he was deeply resented for his role in the Stalinist terror apparatus.