C++ :: Passing A Function Pointer As Template Argument To A Class

I have in the past written code for templated functions where one function argument can be either a function pointer or a Functor. Works pretty straightforward.

Now I am in a situation where I am actually trying to pass a function pointer as template argument to a class. Unfortunately this does not work, I can pass the Functor class but not the function pointer. Below code illustrates the issue:

Code:
#include <string>
#include <iostream>
#include <sstream>
#include <cstdlib>
// For demonstration
const char * external_library_call() {
return "FFFF";

[Code] .....

The idea is to have the definition of the Record class simple and readable and have a maintainable way to add auto-conversion functions to the class. So the lines I commented out are the desirable way how I want my code to look. Unfortunately I could not come up with any way that was close to readable for solving this.