WI CIA accidentally kills Syngman Rhee

So I was reading Tim Weiner's Legacy of Ashes and came across an incident shortly after the end of the Korean War when Syngman Rhee was on a yacht and sailing by an island that the CIA was using to train paramilitaries. The paramilitaries according to Weiner opened fire on Rhee's boat due to miscommunication. No one was hurt, but what if Rhee was killed during this incense and it became publicly known that the CIA was responsible? Ramifications for South Korea, US and Cold War at large?
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.
Might produce an earlier and smoother transition to democracy in South Korea with important opposition politicians such as Shin Ik-Hee, Cho Byeong Ok, and Cho Bong Am all still alive.
Vice President Ham Tae-Yeong becomes President, but he was very old. Most importantly, he had no political base on his own. The ruling Liberal Party was entirely built up on the basis of cult of personality around of Rhee, and Ham Tae-Yeong, a mere Vice President, was elected solely because of his inability to pose a threat. The dictatorship wasn't firmly established yet, and Ham wasn't someone who could replace Rhee as the leadership, then there's a general election coming in 1954, so a lame duck phenomenon is pretty much guaranteed. At the same time, if Rhee's successors avoid the practice of exploiting military's regional division for political capitalization, the possibility of military coup is substantially reduced as well.

Around this time, a significant part of the Liberal Party was under influence of Lee Beom-Seok, a known fascist sympathizer, and his National Youth Association, so it would be interesting to see if Lee could inherit Rhee's cult of personality and the party as whole. But more likely outcome is the division of the party between the NYA faction and non-NYA, more moderate faction including Lee Gi-Beung before the general election of 1954. Rhee was still popular in 1953 for his firm commitment for war and unification despite his mismanagement of the war, so for the Liberal Party successors it wouldn't be hard to translate the former President's popularity into vote.