no not all black lights contain uv.... but you need to do research and make sure the one you get doesn't.... the cheaper black lights are nothing more then a normal florescent light that has a purple/black paint on them.....others will give off small small amounts of uvc....and if you get the led version on the black light most of them give off full spectrum uv (uva,uvb and uvc)..... but honestly don't take my word for it.. do a search and research for your self..... I may have to find find what page I found most of my info on and post a link to it here... I believe I found it on either about.com or wikipedia either way I did days of research to make sure the info I found was correct and not just some no bodies believe....
here is one quick link... this is one of the main places I found what I would call good "real info"http://en.wikipedia.org/wiki/Black_light
please let me know what you understand after the reading..