If I may add a different suggestion: have you considered hacking one of the old consoles that you have/can buy used to enable retro gaming? A used Wii or Wii U for instance have great wireless controllers available, especially used Wiis without the games and accessories are dirt cheap. The process is very simple, just do a quick google. Basically, hack an old console, load the ROMs you have, get an appropriate wireless controller (8bitdo makes A LOT of compatible wireless gamepads), and you’re good to go.
Here is an example, for the Wii U, though the Wii is probably even easier (but SD)
You could also get the games using the virtual console offerings for the Switch if you don’t want to mess with ROMs. I know the switch has that adapter thing that holds the nunchucks in a ‘classic controller’ gamepad form. Even very old consoles sometimes have great retro gaming or homebrew options, the classic Xbox to name one example.
All in all I think this would be the fastest and maybe even cheapest option.
Also, kudos for nurturing the love of video games in your son.