I was given a crappy blunt disposable by my Mother, who didn't want to give me one, but the many kids teasing me made her reluctantly give me one.
Of the ones I have used, the best one I have found that has so far NOT EVER cut me, and gave a nice shave was the Schick Hydrosilk. I ended up getting it as a freebie with a Target.com order. Prior to that I was using the Men's Gillette Mach 4 Turbo, as it shaved very coarse hair smoothly without nicking my skin.
Personally, I also use Nad's hair removal gel(it's all natural, and has never given my skin any issues, and I have very sensitive skin). If you are worried about her accidentally cutting herself, you may wish to go that route. I recommend it for use on underarms. It's a sugar based gel, and the mango shea lotion for use afterward makes the skin feel refreshed.
Hope this helps.