Should one use oil with all stones??
(specifically Wyoming and Arkansas)

BEJ--

There should be something used to keep the material cut by the stone in solution so it'll stay sharp and clean.

Automatic Transmission Fluid (ATF) is the preferred oil with kerosene a second choice. ATF is very easy on the hands.

Good quality stoning oil is available from Gessweins or Congress and other suppliers of tools for toolmakers and moldmakers. If not using that I would use the small cans of oil from Buck or other folks that sell stones or knives.

Try ATF mixed 3 parts to 1 part mineral spirits (paint thinner).

Also, if your stones are gummed or loaded up sneak them into the dishwasher.