Will the Cooler Master Hyper H412R cool better than the 8600K’s stock cooler?

No. CM Hyper H412R is designed to be used for cpus up to 100W TDP.
8600K is 95W TDP. Intel stock cooler can handle up to 130W TDP. BTW - there are bunch of different Intel stock coolers, i5-8600k don't have cooler bundled with it.

For overclocking choose something better than H412R.