Good evening.
For a one off, reshape and to save all the dollars in drills and presses etc.

Try your local hardware store.
Then find or ask for ..belt sander... belts.
They came in a number of grades.

Buy 2, a course and a smooth grade.
Cut the belts so that you now have a long strap like section of, whatever grade ?
Then wrap it around the cork
and DON'T NOT apply much pressure, just a soft back and forward.

Then the smooth belt the same.

Arr too easy, when you know how.

Kind regards,
UB