Colored Shelves for Chin

I recently purchased some colored wood accessories for my chins cage.. They are colored with food coloring. When taking everything out of the package, i noticed my hands were getting stained by the color. I've been nervous about putting it in my chins cage because i don't want it to stain the white fur on her belly. will it stain her? Is there anything I can do to remove any excess color?



Also, if my chin was to pee on a colored shelf, would the wetness cause the color to transfer to her fur more easily?