Execute Stored Procedure that cannot be manually stopped
What you want is, by definition, impossible. Because the definition of admin is: the user to which no privilege can be denied. Therefore any attempt to do something that has the phrase 'admin cannot' is flawed from the get go, because the admin will, simply, always 'can'. 

There are more fallacies in your reasoning, like the belief that there is any way to make privilege decision based on untrusted input. Case in point, the requirement that The stored procedure must be invoked from SSMS ONLY.. This is a security decision (privilege to run the procedure) based on an untrusted input (the APP_NAME()).

What I suggest is rather than ask us how to implement what you already concluded must be the solution, better lay down your requirements and let us suggest possible solutions to your problem.