Cross compile project using pybind11 for windows on Linux using MinGW

[rhvarrier]

I have a C++ library for which I'm using pybind11 to generate Python bindings. Currently I'm compiling on Linux x86 host for the same target using gcc and everything works fine.
I want to port my library (which only depends on C ++ std libraries) to Windows and I was to keep my current Linux development environment and cross compile the library for Windows using MinGW (from MXE). However when I try to build the python bindings using pybind11, the compilation fails as MinGW cannot find a compatible Python library.
My question is as follows:

1. Has anyone else had a similar issue and if so is there a workaround. I tried compiling CPython using MinGW but it seems quite tedious and not well supported by current Python versions (> 3.9)
2. Is there a way that pybind11 generated module does not link to Python at all (I could just provide the necessary header files) But at runtime (i.e. when a python script that imports the module gets interpreted), it automatically loads the Python DLL (the one that ships with Python and was most probably compiled with MSVC). If this works I could just distribute by python module along with a compatible Python DLL
   If there is a 3rd option I would be most welcome as well (N.B. I cannot compile on Windows and I need to keep my a cross compilation environment (not necessarily MXE)