[...]as it asks for a window handle, which I do not necessarily have in the process.
Maybe the problem you are having is that you haven't seen how to get the window from SFML:
window.getSystemHandle();
https://www.sfml-dev.org/documentation/2.5.1/classsf_1_1Window.php#ad2fa6be5104ec0bfe79af7a5f524ea90
[...]as it asks for a window handle, which I do not necessarily have in the process.
Maybe the problem you are having is that you haven't seen how to get the window from SFML:
window.getSystemHandle();
https://www.sfml-dev.org/documentation/2.5.1/classsf_1_1Window.php#ad2fa6be5104ec0bfe79af7a5f524ea90
No, the program has no windows. However you are right in that a window is NECESSARY to use the windows api, even if that window isn't used for anything else and hidden from view.