The answer is that you cannot use the Immersion Oil without water-mounting the coverslip.
I tried it.
The water-mount "glues" the coverslip to the slide, effectively anchoring it in place. Without doing this, when you add the Immersion Oil, the coverslip will slide around because the oil "grabs" the coverslip. When you pan the stage, the coverslip is stuck to the lens and the slide on the stage is moved around but the coverslip doesn't move because it's adhered to the lens.
When you water-mount the coverslip, it is anchored so solidly that it is actually even difficult to push it with your fingernail.
Conclusion: No Immersion Oil without a water-mount!