Good thought, but no, there is no opposite for show or no show. You can use a script to hide elements from certain users but in this case I don't think it wouldn't work because registered users have more rights than all users.
Example of hiding an element on a page - I have the Excel button hidden on our Tags. We have users whom should not be able to export information to Excel as those exports include birth dates and things we don't allow them to see. The script I have on an Advanced HTML Module on Tags is:
I have security set to all the lower rights roles who should not see the Excel button. Anyone with higher rights, who sees all the info about people can see the button and use it.