Black light will not help. Black light is not killing algeas. I heard about BL can increase fish diseases and shorten their life duration.
What you can use is a UV Sterilization for when you have green water. Note that UV Sterelizers don't have same wavelenghts of blacklights, they are optimized for sterilization. Water need to be in contact with the UV Lamp, so I don't think a simple black light over the tank will help.
For diseases linked to aquarium water, I don't think you can get a disease if you don't have cuts on your hands. In my case, I already have get Hair algea combined to green algea on glass and greenwater (so green that i can't see the fish) and I neved had health problems. It's the first time I heard somebody got a disease from his tank, and I think maybe the disease your dude got was probably not from his/her tank.
Note that algeas are plants and they are not toxic if you touch them. But I will not recommand you drink your fish water. I already have drink a shooter of my aquarium water, I was drunk, I won 10$ for doing this, and I had not been sick.
Personally, I would not fear to put arms in water. Clean both hands and arms before you put it in the water, and clean them after too. You must not introduce arm grease in water. Make sure you rinse well so you don't put soap in the water.
If you're talking about Green spots algea on the glass is a sign of balance in a tank. They are hard to remove with a sponge/scrub, people usually use a razor blade for doing this (if it's glass aquarium).
So:
Should I put a UV light on my tank? I will say no.
Do they work? I will say no because of the wavelenght
Do they hurt the fish? I will say yes but i'm not 100% sure.
I am also afraid to put my arms in the water.Not sure algea or bacterials from the tank is harmfull except if you allergic to something in it.