C++ Calling the right free function from a base pointer/reference

Let a class hierarchy :

class Base { virtual ~Base() throw(); };

class DerivedA : public Base { };

class DerivedB : public Base { };

I would like to have some code specific to each of these derived classes. However that code also being specific to the application that makes use of this class hierarchy, I do not want to embbed this derived-class-specific code into these derived classes. To avoid doing so, I thought about writing free functions :

void DerivedASpecificWork( DerivedA da );

void DerivedBSpecificWork( DerivedA da );

However, when given an instance of a derived class through a reference/pointer to a Base, I do not have access to the actual type of the instance, and thus cannot call the proper Derived*SpecificWork() function.

I would like to know if there is nome kind of design pattern that would allow me to call a derived-class-specific function without knowing the actual type of the instance, i.e having the same mechanism as virtual functions provide, but without having these virtual functions that would require me to embbed application-specific code into that class hierarchy.

Actually, why I want to do that is to provide informations about an exception that occured within a natively implemented function called by a Lua script. Each exception carrying its own set of information, the way I want to represent the error within the script depends on the type of the exception. I could create a pure virtual method in the base class that would be implemented by derived classes, but this would require me to embbed Lua-related code into my exception hierarchy, which I do not want to do since the Lua is specific to one of the application using that exception hierarchy.

Also I cannot use C++11.

Thank you.