What would be preferable for South Korea, if they had a choice: a North Korea publicly seeking reunification on the South's terms, or a North Korean puppet state that remains independent but the South controls behind the scenes?
Your latter option sounds a lot less like a "puppet state" per se than it does a "gradual/controlled reunification", which is what I think is most likely to happen as is: that the North becomes a de facto Southern protectorate after the "fall of the regime" (whatever that entails) in a nominal confederation but essentially separate from the South. Over a period of 10-20 years North would be developed to a level where full reunification would be non-cataclysmic.
The Northerners would still experience a dramatic rise in liberties, their standard of living, but would at the same time be used to (for a time) by sheer custom to curtailments on their rights that most would consider excessive but would prevent the sort of catastrophe most imagine happening in the case of a sudden reunification (for example, I imagine people needing a permit, much as is the case with the Chinese
Houkou system, to move to the South). I easily see the North, which was historically the more industrially active of the two regions, becoming the next massive center for low cost manufacturing.
