Dawn dish soap is the way to go. If you are talking about the bone matter way into the nasal chamber…..get it out. It is cartilage and will discolor in due time. Check out other European mounts and you will see the nasal passage is clean.
Bleach softens and makes the skull porous. I have done deer, elk, and bear with the dawn dish soap and I have some awesome looking skulls. If the skull does not turn out as white as you want, purchase some basic white from your local hair salon and paint the paste onto the skull, let sit then rinse it off.
The teeth will also fall out but they are easy to put back in, they only go in one way.
An air compressor might be messy but is a great tool for clean flesh on the bones and holes. Wear glasses and old cloths when using an air compressor.
Keep the horns out of the solution and wrap them in aluminum foil. It will keep the antlers original.