Dammit, you had to mention how it would happen, I was busy picturing someone in Langley mixing up a cigar box and Rhee exploding.
As for the ramifications, well it depends on how South Korea plays it. The beauty of the 50's is that the knowledge that the CIA did it could be kept from the general public, it would take work and get out in time, but immediately it could be prevented. The South Korean military could chose to do anything from "Military Junta" to "Rhee is gone, proper democratic institutions" and any number of steps in between, the only thing they won't do is open the gates to the North. Only thing I can say for certain for the South, is that things would be different.
I'd imagine that the North would try and probe the DMZ in this event, might even get a couple of "small" breakthroughs, but that would be as far as they go. Depending on circumstances, the CIA might even be able to make it look like Rhee hit a rogue mine from the North and the North would take that and run with it as propaganda.