If you want to only use the netCDF-4 API to copy any netCDF-4 file, even those with variables that use arbitrary user-defined types, that's a difficult problem. The netCDF4 module at netcdf4-python.googlecode.com currently lacks support for compound types that have variable-length members or variable-length types of a compound base type, for example.
The nccopy utility that is available with the netCDF-4 C distribution shows it is possible to copy an arbitrary netCDF-4 file using only the C netCDF-4 API, but that's because the C API fully supports the netCDF-4 data model. If you limit your goal to copying netCDF-4 files that only use flat types supported by the googlecode module, the algorithm used in nccopy.c should work fine and should be well-suited to a more elegant implementation in Python.
A less ambitious project that would be even easier is a Python program that would copy any netCDF "classic format" file, because the classic model supported by netCDF-3 has no user-defined types or recursive types. This program would even work for netCDF-4 classic model files that also use performance features such as compression and chunking.