If having no nickname isn't a possibility, the Green and White is the next best choice.
It allows the old guard to still feel an attachment to fighting Sioux, as green and white are just colors.... Meanwhile the PC crowd can run with Green and White and design whatever logos they want, while I wear my Sioux gear.... Which happens to be colored.... Yes, green and white.
The Syracuse Orangemen changed to the Orange, and appear to be quite successful just having a color as their new name.