I use diluted Simple Green for everything, it is non toxic and I like the smell. You could use plain water with a little soap, And when I can’t find anything just plain water… I left once my diamond stoned submerged in water for a week or two, and it didn’t rusted them, but to prevent I always dry the with a hair dryer prior to storing.
By the way, I have also used a very diluted solution of lysol and seems to work fine. I only use it to prevent friction and to surface the waste iron that seems to deposit in the waterstones and diamondstones.
In summary, don’t worry, use what you have on hand.
Found the following on the DMT site in their FAQ section:
I know it says to use the sharpener dry or with water, but can I use oil anyway? Can I store my DMT stone in kerosene?
While we recommend you use DMT® products dry or with water only, it is acceptable to use a variety of lubricants when sharpening with DMT® products. Mineral oil, mineral spirits, kerosene, WD40 can all be used without harming your DMT® sharpener. We do not recommend storing your DMT® sharpener in kerosene. DMT® recommends that you always wipe your Diamond and Unbreakable Ceramic Sharpeners clean and store dry after use.