If you previously installed the native version, you will need to uninstall that first because Steam doesn't allow both versions to be installed at the same time. (Library > Right click game > Manage > Uninstall).
Next, you need to force Steam to use the Proton version (Library > Right click game > Properties > check box for "Force ... Steam Play compatibilty tool" > Choose any version from drop-down > OK). For reference, my version was "Proton 5-0-9" but newer is probably better.
Then install TW2 (Library > Right click game > Install); Steam will now download the Proton version. I also recommend disabling the Steam Overlay after install (Library > Right click game > Properties > uncheck "Enable Steam Overlay" > OK)
Initially, it would not launch but after consulting protondb I found that I had to run cp -a "${STEAMDIR}/common/the witcher 2/bin/config"/* "${STEAMDIR}/compatdata/20920/pfx/drive_c/users/steamuser/My Documents/Witcher 2/Config/" where STEAMDIR is whatever you have in Settings > Download > Steam Library Folders (default is ~/.local/share/Steam/steamapps).
At this point, I could get to the launcher but I had a black box over launcher text and I had clicked upper right where I guessed exit button would be and it closed. Go to Library > Right click game > Properties > Set Launch Options and use: PROTON_USE_D9VK=1 %command% then click OK to save and OK again to exit properties. If you still get the black square in the center of the screen, drag the launcher to the left/right and you will be able to see.
If you are playing with keyboard and mouse OR if you plan on using gamepad to k/m mapping software such as antimicro * (github | deb files on LaunchPad), then you can skip this step. Launch the game. If controller works in the menus, you need to go to Options > Controls > and change from Keyboard to Gamepad; otherwise, the controller will only work in main menu but will be IGNORED once you get in-game. I was using a wireless xbox 360 controller and had the xboxdrv package already installed -- mine worked fine after changing this option. If that doesn't work, some folks reported better success for Steam controllers by launching from Steam's Big Picture Mode instead : see here.
* The deb file for artful installs fine for me on Linux Mint 19.3 and also worked for installing it on LM 20 in a VM. If you prefer modifying an AntiMicro preset rather than creating one from scratch, I also found 3 "mod" downloads on nexus which provided AntiMicro profiles (*.amgp files): 761-Quick signs for The Witcher 2 - Enhanced gamepad layout by MaxBelmont, 767-Witcher 2 Quickcast Enhanced Gamepad Mod by ozz61, and 848-Improved controls for gamepad by ProbeAway. Of the 3, the last one seemed to be the most difference from vanilla controls.
