I use WD40 on a small DMT hone to touch up chisels, and it works very well. No issues with build up of a skin - I figure that adding fresh WD40 and using the stone clears any residue from previous applications.
If I have a water supply available I use water, and dab the stones dry afterwards. You may get a bit of rust on the stone, but it's only the material removed from whatever you sharpened that rusts - the diamond material and substrate seem unharmed. If the stones get gungy a stiff pencil erasor does a great job of cleaning up, as does a PCB etchant-resist cleaning block.
If I have a water supply available I use water, and dab the stones dry afterwards. You may get a bit of rust on the stone, but it's only the material removed from whatever you sharpened that rusts - the diamond material and substrate seem unharmed. If the stones get gungy a stiff pencil erasor does a great job of cleaning up, as does a PCB etchant-resist cleaning block.