Realistically, no. There is a fellow that has tried editing some files for SH4, but I was not able to find his thread as of yet. Grenso over in the SH5 side of things replied to another fellow with an ultra-wide screen, and pointed him at
Post #4 - SH5 on Ultrawide screen?, but that might be SH5-specific. There are several attempts over in SH3, but those would definitely not work with SH4. Near as I can tell, the SH4 game can do a 4:3, or a 5:4 or a 16:9 resolution. Nothing else 'natively'. All the utilities you might be able to find for an ultra-wide set-up is "fooling" the game into a display resolution.
I have a 32 inch 4K (3840x2160) 16:9 monitor for my Windows 10-64, and I have the screen set at that, with a 125% "zoom" and large icons, and the desktop is fine. Lot's of real estate to work with also. However, doing SH4 at that is not good on my eyes either (not even the 2k 2560x1600). I cannot read the gauges at those sizes... So I keep my screen resolution for Windows, but choose 1920x1080 for the game itself. I have to set the SH4.exe Properties to "Windows XP SP2" Compatibility, and "Disable fullscreen optimizations". On the "Change high DPI settings" button, I have "Override high DPI scaling behavior" and Scaling performed by "Applicatioin".
Now, you have close to a 21:9 resolution (31:13??), so you will not be able to "fill" the screen with the game without extra software, which as mentioned, sometimes works, sometimes does not. I would go ahead and run your display at what you want your desktop at. "Native" is best, but you might not want to mess with that Windows "zoom" stuff either, and it might complicate things with the zoom when in SH4 also, which can sometimes (sometimes... sigh) be 'fixed' with that "Program DPI at the top of the High DPI page. You would set that to "I open this program" - but I have run into issues using that also... Anyway, set your Windows resolution, then run the game. Go to the display Options inside the game, and set it to 1920x1080, but also set the "Windowed Mode". That way, you should get a 16:9 screen that is scaled-up to your screen height, but will not fully cover the width. You will most likely have to noodle with the SH4.exe Properties though. But that is about the easiest way to go...
