I would avoid food dyes completely.
I have olive skin with dark hair, so I use Boots face & body hair lightner, which is excellent. It's always on offer and you also get points. A little goes a long way, and it lasts ages on me, especially during the summer months when the sun naturally turns your hair slightly lighter.
The only downside to it is the way you apply it - mix 2 creams together, apply, leave for 10 mins, and wash off. I've used it on my arms before and noticed that it slightly lightened the skin in the areas I had applied it. It fades after an hour, but it's worth bearing in mind if you are going out immediately afterwards.
The only other product I have used is for body hair and is a lotion from Spain. It smells a little bit, but the idea is that you put it on, wait for it to dry, and then that's it! It contains natural ingredients like lemon juice, so the theory behind it is that it activates in sunlight.