Black light and UV light are not two different things, Both are UV, just black lights or UV torches(I have one, it's cool) put out UV-A which is harmless. UV-B is higher frequency and is most of what gives tans and UV-C is really nasty. Used in UV sterilizers, Flouro lights and MHs produce UV-C. But in fluoros it's blocked by the coating of the tube which then fluoresces and gives off the light you want and in MHs by the cover glass.
Of course, it's not a sharp cutoff between the 3 types, so high end UV-A would be similar to low end UV-B...
Either way, a blacklight isn't going to do any damage to your fish.