10000 km Radio Polarization
There's no way to know. The polarization of the signal is rotated as it passes through the ionosphere, with the amount of rotation depending on the frequency, the path length through the ionosphere, and the electron density at every point along the way. These are subject to change, sometimes rapidly, and I believe that over typical skywave paths at HF frequencies, the total rotation is quite a bit more than 360°, so that even fractionally small shifts in the path length (caused by changes in the effective reflection height) or electron profile can alter the received polarization by 90°.
For this reason, every resource I know of treats the polarization of any signal received via skywave as effectively random.