This isn't very easy to do and may not work for certain games at all.
The first step would be to change your desktop monitor resolution to the desired one. This can be done with specialized tools(e.g. Custom Resolution Utility) or possibly the GPU tool (eg Nvidia control panel). You need to select a custom resolution. This will result in black bars.
Second step is to stretch this resolution to full panel, which can be done using the GPU tool. Look for full scaling or "Adjust desktop size and position".
You've now changed your native resolution to a scaled/stretched 3840x1080 or 1920x2160. The moment of truth is next. Launch the game, you should now be able to select the resolution you just set your monitor to and it should behave exactly the same. If not, the game doesn't support wonky resolutions at all. If yes, it may be possible, that the game saves this resolution and you can revert to standard on your desktop without it affecting the game.
However, I'd still advise to pick a lower native resolution than going for a wonky stretched one. The standard resolution 2560x1440, which is supported by every game is about 89% the pixels of your proposed stretched ones and will likely look better, as doing a horizontal or vertical stretch just isn't as good as a native 16:9 resolution.