Is there a setting to change Directory Opus's file copy/move handler to the system default or TeraCopy?
I'm using version 12.4.
There isn't a one-place change, but you can change the various toolbar buttons and drag & drop events (at least in Opus Pro; not all are editable in Opus Light).
Why do you want to change it?
Just a personal preference of mine for the UI layout and progress bar style of TeraCopy.
It'd be very useful to have a simple "Use default file copy handler" checkbox option 
No "default copy handler", that would only lead into problems. If you prefer TeraCopy, just build the buttons you need. I think there're already some in "buttons/toolbars"-forum.