I know that I wouldn't use the colour green in working with cancer, because it is a colour of growth, however having said that, I know that reiki energy is intelligent, and I'm sure that the energy one works with using QT is intelligent too, so I would assume that it would do what is needed to heal, not help the cancer grow.
BUT, I'm still very wary about using Reiki on someone with cancer, especially if they are on chemo, because the side effects of that are horrific and the last thing you want is to add a possible 'healing crisis' from reiki (or any other energy healing) to it....
I'd say think long and hard about it, commune with your guides and work slow and gentle if you do proceed...