So I tried running Fallout 1 in dosbox-svn, and the performance didn't feel great tbh, not too smooth.
What I've got now is fallout1-ce built for Switch Linux, I fixed a bug for duplicated cursor movements with the touchscreen, it's still a bit funny about registering a click when you start a movement on the touchscreen but it seems playable, only with touchscreen for mouse movements so far, controller support would be more work. Or you can use an actual mouse if it's connected and working on your Switch before you run the game.
If you're running Linux on your Switch, you can copy the files from a Windows version of Fallout 1 into a directory on your Switch, then put these files in the same directory and run fallout-ce. I've included config files for the screen resolution and the right file paths, tho you can edit the paths in fallout.cfg if they don't match your version of the game, and you can set subtitles=0 if you don't want subs on the videos (they were off by default, I turned them on).
edit: Added a newer build which disables input from a real mouse, in order for touch input to work correctly, so you don't get a false click when you start moving the cursor. This problem is caused by the messy way the game handles input, combined with a weird quirk/possible bug of SDL2, and I haven't found a clean way to work around it so this will do me for now. Use the "disable real mouse" build if you want to play with touchscreen, use the other build if you want to use an actual mouse.