Dog, I agree; naphtha (aka Zippo lighter fluid) is a 'go-to' degreaser.
Stoddard, I believe, is chemically somewhere between octane (gasoline) and pentadecane (15-carbon chain) and will eventually evap.
It's the proprietary-unknown ingredients in WD-40 that may stay behind and eventually gum up a stone (or your Glock).
One may argue that a firearm gets an awful lot of powder residue which mixes with the WD-40 to form a paste, etc. And that's true, but it's also true that an Arkansas stone gets an awful lot of metallic micro-particles that might do the same thing.
Mineral oil is safe in that regard because it's a long-chain hydrocarbon (aka paraffin) that will stay liquid forever and won't oxidize. It will eventually form a stiff paste with all the metal particles that have been cut by the stone. But since it's chemically inert, it's always be easy to wash off using Zippo fluid.
An cheaper alternative to Zippo fluid is 'VM&P Naphtha' from Home Depot, Lowes, Ace, etc.
Three things every guy needs: Duct Tape, a good pocketknife, and a bottle of Zippo lighter fluid.