Arcade Controllers is a broad category that encompasses the vast majority of third party controllers that are used for playing arcade games, arcade style games or fighting games. <br>
As long as you can connect the arcade solution to USB, it has working udev/drivers and xinput then it should work with RetroDECK.
**Always check for Linux Support**<br>
Just to be safe, it is better before you buy anything to double check if there is Linux support for it.
Wireless Fight Sticks can be a hit or miss depending on if they require external configuration software.
Many USB Fight Sticks work nativly on Linux without much of a configuration. There might be need for a slight input remapping if they are a console version of a Fight Stick.
There are several predone kits to make your own PC connected Arcade Machine. <br>
They a majorty of them use a standard USB interface to connect to the PC and many times the same connector board as in the standalone Fight Sticks while the trackballs has a seperate USB connection that simulates a mouse.
There should not be any major issues connecting these with RetroDECK except maybe a controller remapping.