If you're not overclocking the only concern you might have over not using the stock cooler is noise reduction. Any 120mm or 140mm third party cooler will take care of that and still allow you moderate overclocking headroom should you choose to do that down the road. I have both a Noctua NH-D15 and a Thermalright True Spirit 140. The True Spirit is a little quieter, much less bulky and still very capable in cooling (oh, and considerably cheaper). https://www.amazon.com/Thermalright-True-Spirit-140-Power/dp/B00IYEEOMO/ref=cm_cr_arp_d_product_top?ie=UTF8
It gets mixed reviews from those who purchase it on both Amazon and Newegg. Is there any reason why you are focused on that model? Lots happy initial users turning to to complaints about the pump dying within a few months.
AIO coolers are not particularly effective, along with other issues.
Your case can handle an air cooler as tall as 186mm.
I suggest a noctua NH-U14s or NH-U15s if you will be aggressively overclocking.
They will cool better, cost less, be quieter, and will not leak.
Here are the specs: http://noctua.at/en/tdp-guide
I agree with Geofelt that the Noctua coolers are going to get it done. They are relatively silent. They do a great job cooling. Their pumps won't break after 5 months like it seems many Kraken x42 users reported.
If you're not overclocking the only concern you might have over not using the stock cooler is noise reduction. Any 120mm or 140mm third party cooler will take care of that and still allow you moderate overclocking headroom should you choose to do that down the road. I have both a Noctua NH-D15 and a Thermalright True Spirit 140. The True Spirit is a little quieter, much less bulky and still very capable in cooling (oh, and considerably cheaper). https://www.amazon.com/Thermalright-True-Spirit-140-Power/dp/B00IYEEOMO/ref=cm_cr_arp_d_product_top?ie=UTF8
K processors do not come with stock coolers.
Also, the I7-7700K runs at stock at 4.2, a clock rate not too much lower than what overclocking might be.
I think it needs a better than average cooler.