Hey,
DAPI/Hoechst excitation require UV light, so if there's a UV filter in front of your camera, you'll see only the fluorescence signal.
However, common glass is not transparent to UV, so it might be that if you're using cheap glassware in the beam path you'll have a problem.
The 100X objective does not let much light go through it, but Hoechst and DAPI have a very high signal-to-noise ratio, they're very bright, so even in an hacked system there shouldn't be much of a problem.
You can find microscope cameras around, but does your microscope allow for a camera? Is it a trinocular? You can spend additional money for a camera and a C-Mount and hack light source and filters, but probably at that point the cost becomes too high.
If you wanna go DIY, then I would hack the system completely. You can just stick a raspberry Pi camera in front of the ocular (possibly with a 20X magnification if you have it) and it should come with a UV filter (I don't know how much useful).
There are UV leds that you could use for illumination, you have to make sure that they would provide enough light.
Filters in your case is easy, you can find UV filters.
The solution with the UV light source in one ocular makes sense and it's probably the only one available to you (beside the paralens): you need the light to point away from your eyes and have the fluorescence reflected back, differently to what you are probably used to in brightfield.
Best,
ukitel