Hi Bjielsl, welcome to the forum!
A common blacklight won't do anything to the algae. Neither will an UV LED. They both operate at too long a wavelength of light.
A UV sterilizer bulb operates at a very specific and shorter wavelength, optimized to destroy organic material. Like the part of sunlight that produces sunburns, but even more destructive.
Now what if you get a true sterilizer bulb that fits into a common fixture? As it happens, I have one.
So I attempted to use it to cure a greenwater bloom. Knowing how dangerous the light was, I improvised a shield that water from the HOB filters would flow over, but protect the rest of the aquarium underneath from exposure. Being careful never to look at it without eye protection (it will easily burn your corneas), I ran it overnight.
It did a spectacular job of eliminating the greenwater. But apparently a bit of the light leaked past the shield, and it was enough to burn the tops of all my fishes. Then secondary infections set in. After much medication, I managed to nurse them back to health; but to this day I have several black guppies with noticeable white patches on top.
As much as I like trying to DIY strange things, I admit now it's best not to attempt any DIY UV setup. I'm not aware of anyone else who's done it successfully either. Go with a commercial unit. Or try other methods (blackouts, diatom filtration, etc.), though your chance of success is less.