I surely like all AH ideas related to Czechoslovakia, but in this case I can't see it as plausible with a POD after the German surrender.
First of all, there was no Czech and Slovak population in official terms, they were part of single Czechoslovak nation until 1960's. There are mentions of Slovak independent movement after war, but I don't think it was very strong (the idea was discredited by the fascist state after all). The split would deepen the trauma, not heal it!
Furthemore I don't believe it would have been possible for the Czechoslovakian leadership to accomplish the split even if they wanted to. Why would the Soviets allow such a think? What would this mean for all the former independent nations that became parts of USSR in past years?
Even if this somehow happen, the split wouldn't last long. In the 1946 elections OTL the communist party won in both parts of Czechia, but was beaten hard in Slovakia. I guess the Gottwald's government would quickly reevaluate the split as an illegal action and take measures to help their Slovak comrades to seize power and reunite Czechoslovakia, maybe forming a federation few decades earlier than OTL.