Script that creates or deletes a desktop shortcut depending on the user that is logged in

Hi Scripting Guru's,

I don't have much background in scripting and I'm looking for some help.  I work in a public library that has a generic login for public users and specific logins to our domain for staff and members.  We want to either create a desktop link to a URL that provides information on how to print for our "Public" users or delete the link if not logged in as "Public" user.

TLDR: 

A script that would delete a desktop shortcut to a URL if the current user is not "Public"

or 

A script that would create a desktop shortcut to a URL if the current user is "Public"

The specific computers would be on a domain, not sure if that would affect the script.  

Windows 7 machines by the way,

Many, many thanks!