I'd certainly try
Analyze -> Cell analysis -> Cell + Membrane detection.
It only works with hematoxylin & DAB staining, but can create cell objects based purely on membrane staining even if no nucleus is visible. It was created when working with HER-2 staining.
For image analysis in general, I'd much rather work with fluorescence images, and would ideally like the 2-color IF idea. Then the general Cell detection command can be used - although as microscopyra says, the cells are created based only on nucleus detection and distance, and without actually using the information in the other channel. This might still be ok though, and give more options for a day in the future when QuPath may have a new and improved cell detection command working for fluorescence images...
Finally, when using your current image with Cell detection you should see an option in the dialog box Exclude DAB. This tells QuPath to avoid detecting a nucleus if it finds a stronger signal in the DAB. It could be a bit hit-and-miss (limited by how well the stains could be separated), but is probably worth a try.