Very strange upgrade. You are halving the number of cpu threads and gaining single core performance. More of a side grade than an upgrade unless you have a specific task in mind that relies on single core performance.
At single threaded activities yes it does but for multitasking or highly threaded applications the difference is fairly small. What is the pc used for? Why not the i5 10600k that is also 6 core 12 thread or wait for the new AMD 5000 series announcement on the 8th October.
Adding to what others said, if you have a Ryzen 1600X, and it seems you need more single core performance, why going for a death platform and a no-HT CPU like the core i5 9600K, when you could probably update the motherboard BIOS and put in a Ryzen 5 3600 or 3600X?
Or, why not wait till october 8 when AMD launch Zen 3 and you may be able to get something equal to the i5 10600K for lowerish price?
Hell yes the liquid freezer 2 240mm will be enough to cool the i5-9600k. When I had that CPU I used a Corsair H60 to cool it and had absolutely no issues. The liquid freezer 2 240 is quite a step up from the H60 so you'll be good.
In my opinion, the 9600k is a very good gaming CPU at the moment. 6 cores/threads is enough for most games presently. It will begin to struggle when games start to take advantage or more threads though.
The i5 9600K is a great CPU, but we already have games were the lack of HT already show the limitations of this chip.
To put it simple, buying a 6 cores / 6 threads cpu at the end of 2020, is because you know for a fact that the games you play don't need and wont need more than those 6 cores, and you are not planing to play any of the newer games that really push over 6 cores. And of course the fact that the only worth it upgrade will be a Core i9 9900K, if you can find one at a reasonable price later on (Im guessing they will cost equal or more than gold in the next years hehehe).
Just to make things clear, we already have plenty of games that push over 6 cores, and you can see this if you look at the 1% low FPS, which as a result of the limited amount of cores/threads giving worst results than those CPU with 6 cores / 12 threads or higher.
For me 1% lows is whats important, if what somehow indicate game smoothness.