It depends on what you want from the "UV
light". I understand you want to use the UV to
illuminate the subject.
The answer to your question lies in the properties of the diffusers re UV radiation - ie, whether they pass it, or block it.
You could look for some tech specs of the material in this regard, or you could devise some experiment. It would be simple
enough: use your converted flash to record un-diffused subjects illuminated with your UV-enabled flash, then try with the
diffusers interposed. If you get the old
black-cat-on-a-dark-night result, then you have a/n (potentially unwanted) answer.
Or, it may just reduce it a little due to scattering, or... - I suppose you'll let us know