Not sure why you're so tied to a (mostly) fanless build with the upgrade. In my experience, ITX cases need airflow, because most cases aren't designed with fanless operation in mind (unlike your h5).
The NH-P1 does fine with 65W CPUs, but I think you will be disappointed with 105W+ options, especially if you have desires to push your parts a little. Additionally, it performs best with some active airflow, however slight.
I understand the want for quiet operation, so as someone who tried a 65W cooler on a 105W CPU, just get a better cooler. I'm running the Phantom Spirit 120 SE with Noctua fans on an undervolted 5700X3D, got a triple fan 3060ti TUF GPU (with fanstop), a 650W Cooler Master PSU (with fanstop), dual top exhaust Noctua fans, and I'm running custom fan curves with CoolerControl (I'm on Linux, too).
The whole thing sits about a foot from me, and I barely hear it with bare ears. With my non-ANC headphones, I don't hear it at all, unless I'm stress testing it.
Personally, with how hardware prices are going, I wouldn't trade the peace of mind of active cooling for the diminishing returns of passive silence, especially if I planned to actually push the parts at all. Keep those parts cool and working; don't make them rely on their built-in thermal throttling!