Our DMS Software Reengineering Toolkit provides general purpose program parsing, analysis, and transformation capability. It has front ends for a wide variety of languages, including C++.
It has been used to analyze and transforms very complex C++ programs and their header files.
You aren't clear as to what you will do after you "parse the function headers"; normally people want to extract some information or produce another artifact. DMS with its C++ front end can do the parsing; you can configure DMS to do the custom stuff.
As a practical matter, this isn't usually an afternoon's exercise; DMS is a complex beast, because it has to deal with complex beasts such as C++. And I'd expect you to face the same kind of complexity for any tool that can handle C++. The GCC toolchain can clearly handle C++, so you might be able to do it with that (at that same level of complexity) but GCC is designed to be a compiler, and IMHO you will find it a fight to get it do what you want.
Your "output function declarations" goal isn't clear. You want just the function names? You want a function signature? You want all the type declarations on which the function depends? You want all the type declarations on which the function depends, if they are not already present in an existing include file you intend to use?