Onyx is about 6-7 on the hardness scale. Silicon carbide sand paper and carbide tools. It is made into chess sets, and other touristy dust catches in Mexico. Look over the slab with a 10 power magnifier for any since of cracks either starting or filled. As some fill them with just dust and water.
It has been a long time since I made some small pendants with the carbide/diamond type needle files. A light touch when turning I would think as it could come a part while under power.
You can cut it with a diamond saw blade on a wet tile saw or one of those round hack saw blades. keep a wet sponge and swab the area, keeping the dust down when using power tools a mask should be used.
The diamond points that are sold everywhere tools are sold would work on them again use a wet sponge and press the stone against it and use two layers of nitrile gloves if the dremel type tool is a plug in 110volt type. a flex shaft type that can chuck up in a drill press will work to.