The boat plan image on sailboatdata shows a backstay. I would not remove it.
The lines of what you are identifying as a B&R rig do not run far enough to the stern to appear to support the mast.
If your backstay is broken, use the main halyard and run it back to the stern. Make sure it is tight, and let it replace the backstay until you can get your wire backstay repaired. I am conservative when it comes to missing stays. I would probably run two lines from the mast back to the stern to reduce any line stretch impact.
Most B&R-rigged boats have forestays that terminate as fractional rigs. The 34 Hunter has a full foresail, which indicates a masthead rig. Masthead rigs require backstays.