The outside should look like a small cone. The inside sits flush with the caliper. So by your description, I would agree the smaller diameter is on the outside.
You may also try pushing in on the spring clip. This can reduce tension on the pin and allowing you to punch it out. Though that typically requires someone to lend a third hand.
Edit to add, by inside and outside I really mean the inside and outside of the car. Just to clarify.
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