My guess is that the Noctua NH-L9i would probably work well enough at stock clocks, provided your case has adequate ventilation. Intel may officially rate the 8350K as having a 91 watt TDP, but based on reviews, it seems to draw far less than that under load, not drawing much more than 65 watts even when stress-tested. Oftentimes, the TDPs of CPUs won't accurately reflect their power use, and I suspect Intel is simply rounding up to their next higher TDP range, perhaps assuming many people will overclock a K-series CPU.
For comparison, the i5-8500 is rated by Intel as a 65 watt part, and it will boost up to the same 4.0 GHz on four cores, or 3.9 GHz on six cores. On a four-threaded workload, it should be putting out at least as much heat as an 8350K, and on a six-threaded workload it should be putting out significantly more heat, so if Intel considers that to be a 65 watt part, then there's not much reason that the 8350K at stock clocks shouldn't be considered one as well. I suppose it doesn't have the lower base clocks to fall back on in the event that temperatures get too high, but I kind of doubt temperatures would get high enough to be a problem in most systems.
I suspect Noctua didn't actually bother performing detailed tests with the new CPUs for a cooler that they released over five years ago, so they might have just made guesses for their recommendations based on the official TDPs of the processors.
That said, unless your case is small-form-factor and can't fit a larger cooler, a tower cooler would probably be better, even an inexpensive one costing less than that Noctua. You shouldn't need a high-end cooler for this CPU. Even a USD ~$30 tower cooler should be more than enough at stock clocks. Even if you don't overclock, a tower cooler will generally be quieter, and the option for overclocking the processor will be there, assuming you have an overclocking-capable motherboard.