Btw, some management games like OpenTTD and OpenRCT2 (Transport Tycoon and Rollercoaster Tycoon respectively) run on Android, so one can play them on a tablet (a phone is too small for the interface). OpenTTD has lots of additions, potentially making it way more complex than the original game. Dunno about OpenRCT.

Also, back in the time of PlayStation 1, games like Theme Park and Theme Hospital were ported to it and are optimized for the controller — they're easily emulated these days, and run even on handhelds. There are also AeroBiz, Dune 2, Warcraft, and such. PSP had some aero traffic controller games. But management games on older consoles might be rather simplistic compared to modern PC ones.

You can get a used Steam controller on eBay. It's perfect for games like these.I played Dawn of War with one and it worked great.

Try the steam deck or wait for the steam controller! The touchpads work great once you get used to them!

Perhaps a decent touchpad would work better for you. You would only need to fondle the surface and lightly tap it with one or two fingers. But you should investigate in advance if the touchpad allows clicks via tapping, as e.g. some drivers don't support the right click without pressing into the surface, which can be heavy on the wrist. Macbook touchpads worked great for me, being large, responsive, and easy to press.

However, doing lots of scrolling with a touchpad could be rather inconvenient.

If your issue is the position of the hand, you might be interested in vertical mouses, which would allow at least some cursoring, perhaps for more important use-cases. Personally I'm also using the Vimium addon for the browser to avoid the mouse on the web.