Take a look at aniline wood dyes. They hold color well even in direct sunlight and can be mixed with water or alcohol. They come in several colors and/or can be mixed to make other colors. They are usually a powder that can be easily measured. Don't know if they can be mixed directly with cactus juice but just thinking it would not be a problem.
It actually dyes the wood instead a rub in type pigment.
It actually dyes the wood instead a rub in type pigment.