Ok, Preface first, I managed to run PKHeX on Linux, although I haven't test whether the edited save works or not because I didn't have my game atm.
Anyways this (hopefully) should be foolproof, considering I'm one and I managed to do it.... Oh and another disclaimer, don't expect the GUI will be pretty. Btw, I'll try to be as concisely as possible, I'm on my phone writing this.
1. Install PlayOnLinux. It's hassle free Wine from my limited experience, no need to manually set prefix or the like. Foolproof.
2. Download PKHeX and extract the compressed file like you would on Windows.
3. Right click .exe and choose the first option. [please refer to scr1 image]
4. The program will tell you that you missing dotnet (insert dotnet version here) and offer to download it for you by opening your browser (should be legit, it's legit Microsoft website after all).
5. Open the downloaded dotnet using the same step of the 3 step [please refer to scr2 image] and proceed to install it like you would on windows.
6. Magic(?) [scr3 image]
As you can see, the GUI doesn't seems displayed properly but hey, as long as it works some cosmetics imperfections can be overlooked.
Btw, just like I said on first paragraph, I haven't test whether the edited save works or nah because I currently didn't have any Pokemon games on hand, but it should works. If you have any Pokemon save game file you can test and report.
Hopefully this actually works and helping many people that currently on Linux.
Edit:
Tested on Ultra Sun. Editing Pokemon is working [scr4 image].
So far afaik the only problem that I've encountered is in inventory editor, instead limit the items per category if you pick item on the drop-down it shows all items, irregardless of choose category [scr5 image (even if I'm on berries category but the drop-down show all items, although the Give all give category specific items)]
