If I follow the twisty turns of mafia code properly, a visit_url to managecollectionshelves.php MIGHT cause a display case refresh. As long as you don't actually manage anything there.
Logic:
ResponseTextParser.externalUpdate has a capture on managecollectionshelves.php that calls DisplayCaseRequest.parseDisplayArrangement.
DisplayCaseRequest.parseDisplayArrangement will call DisplayCaseManager.update IF it doesn't find action=arrange in the url string.
DisplayCaseManager.update will call DisplayCaseManager.updateShelves as its first step.
DisplayCaseManager.updateShelves calls DisplayCaseManager.clearCache as its first step.
DisplayCaseManager.clearCache wipes KoLConstants.collection and sets DisplayCaseManager.collectionRetrieved to false, which means that it will actually re-parse your display case. It also wipes your headers and shelves.
Based on all that, it appears the only current way to wipe your display case is to either hit the managecollectionshelves page without re-arranging your shelves, or logging out.
Edit: But as Veracity says, it shouldn't be needed. Since it gets updated when you log in, and you shouldn't be able to update it from outside mafia without forcing another log-in afterwards.