Made it work and pushed as ad06c29b37924ecf5eb3bd440c7456cad6415c3b.

Have a look at the redshift package for an example on how to wrap the
final binary to include PYTHONPATH and GI_TYPELIB_PATH from the build
environment.

For this one, I added such a phase:

(add-after 'install 'wrap-screenkey
            (lambda* (#:key outputs #:allow-other-keys)
              (wrap-program
                  (string-append (assoc-ref outputs "out")
"/bin/screenkey")
                `("PYTHONPATH" ":" prefix (,(getenv "PYTHONPATH")))
                `("GI_TYPELIB_PATH"
                  ":" prefix (,(getenv "GI_TYPELIB_PATH"))))
              #t))

Thank you!