So this information didn’t exist anywhere on the Internet that I could find, so I’m posting it here.
The nut that fastens an Atari 2600 paddle controller is 3/8 32. They are also used on electric guitars, I found mine at a music shop. Even better, they had some laying around in the back and gave me one for free. You can also order some on Amazon. If this information helps you like it did me, let me know in the comments, thanksssss.