Hiya, I've just done a search on
Skyscanner &
Expedia, and the flights are all via Lima, taking about 8 hours, but that is still half the time it would take by bus from Cuzco to La Paz via Puno....so it would be your call on what would suit better
Either way, you'll have to do the La Paz to Uyuni stretch by bus, which is around 15 hours.
I also tried other airports which would be closer to Uyuni on arrival (Sucre in Bolivia and Salta in Argentina) but they are much more expensive and aren't direct either.
I think you should plan for La Paz to Uyuni by bus, arriving on evening of 13th, and work backwards from there, deciding what is best for you between plane or bus to get from Cuzco to La Paz....