You can structure a C++ program so that (almost) all the code resides in Header files. It essentially looks like a C# or Java program. However, you do need at least one
You're going outside of the design scope of the language. While you may have some benefits, it's going to eventually bite you in the butt.
C++ is designed for h files having declarations, and cpp files having implementations. Compilers are built around this design.
Yes, people debate whether that's a good architecture, but it's the design. It's better to spend your time on your problem than reinventing new ways to design C++ file architecture.