The entire study is available here. (It's 4 pages)
If you don't want to read it, I have pulled some key points below.
They tested two different UV nail lights that represented 90% of the lights on the market.
" Client hands are likely to be exposed to more UV light while driving their cars than they will receive from UV gel nail services."
There you have it! UV nail lamps, when used correctly, do not cause cancer!