Not sure I understand the question. But it sounds like you want to connect a stand-alone USB controller to a stand-alone USB interface? If so, then no, that won't work.
The only hope you have of getting those other controls onto the interface is by modding them in some fashion. The specific case of a USB / PS/2 trackball is a non-starter without some serious modifications, including bugging out the connection points, trace cutting or desoldering components, etc. The easiest option is to just replace the opto-boards in those trackballs, but the cost of doing that approaches the cost of a new trackball. IOW, don't bother cutting your USB cable. It will just destroy it and you won't be any further ahead.
You can never assume that wiring will be the standard X and Y data lines, it must be verified. For instance, the A1UP spinner/trackball controls are beasts of their own. They typically do not conform to any normal arcade standard in their signal protocols. The white and green wires of a USB cable carry USB formatted serial data, while the X and Y data from an optical control are quadrature encoded pulse-trains.
Wires are just the conduits through which the signals pass, but those signals can be anything.