I am going to assume that you have a clean install of vanilla Commandos 2 on Steam, and you made sure it runs fine by itself, you should always use the new version though, legacy cannot have a higher resolution than 640x480.
Next you want to extract the HD project by launching Commandos 2 HD Project V.1.0 ENG.exe. Notice that you can extract it anywhere, but after that you have to copy all the files and folders into the Commandos 2 install directory (...\Steam\steamapps\common\Commandos 2 Men of Courage). Make sure that CommandosHDLauncher and DATA, and Legacy and OUTPUT and SweetFX folders are on the same level.
Now you can run Launcher.exe directly from this folder. Make sure you don't select horizontal resolution higher than 1920 even if your desktop is higher than that. I had to untick the Reshade effects to be able to run it, you might not have to.
I didn't have to set any compatibility or administrative setting on any exe files.
Good luck and report back please how it went.