This basket can be woven with just plain natural cane without using dyes, the only difference in weaving it this way, is that you will not have the colors. This however, would be a good way to learn just the weave and not have to worry about dyes or color bleeding problems when just beginning to weave. Remember the plain natural cane has a hard outer shell, where as the Hamburg/bleached cane has that outer shell removed. Weaving either plain will do.
Same with the Oklahoma Double Wall, this can very easily be woven without any colors. Once again no worries with dyes or color bleeding. This is how I learned the Oklahoma Double Wall using just plain #2 reed. Then as you get better at the weaving you can branch out into dyes and experiment with colors.