Buffing compounds are abrasive regardless of the "grit".
White diamond is less aggressive than Tripoli and more aggressive than jewelers rouge.The are other compounds that are less aggressive than red rouge.
When working with antler due to its light color a white diamond compound would be more desirable due to the fact any type of residue would not show up.
All that being said.
In the scrimshaw techniques used for centuries, sailors would use the salt embedded sail cloth to polish the material they were going to "etch" their design in.
Scrimshaw is a "negative image process"
The highly polished piece is totally covered with India ink.Once the ink has dried on the polished surface the scrimshander etches the surface leaving the underlying non stained surface show up white as in the case of ivory or bone.The entire piece is etched with the design.Once this is complete the entire area is washed off and reinked.
The ink will be absorbed into the etched areas, the polished ares remain white.
This was all done without buffing compounds.
If the surface is highly polished to the point that nothing will penetrate the surface you can use any compound to "make it shine"
White diamond is a relatively abrasive compound.Jewelers rough would be a better choice provided it is sealed and no pits or rough spots.
The down side is the rouge is red and if you didn't do a good job up to that point you will have a mess.
For Antler I use DICO plastic compound.It is a light blue in color and will not stain most horn.
The shine from the white diamond I am guess is from the polishing effect in conjunction with the wax that carries the abrasive. This wax is not long lasting in the use with a pen.
This is an example of a piece I have used it on.
ANtler buffed with Dico plastic buffing compound