Returning to the Mortuary hilt motifs; it is all a question of timing.
Those hilts were in constant production till well after the regicide, so it is perfectly reasonable to attribute the heads to Charles and Henrietta on Royalist swords produced later. Those royalists would probably enthusiastically flaunt their allegiance to the Crown even after the war was lost.
It's like Colichemardes: everyone says it is not the name of the soldier but that is pre-supposing we are talking about 'hollow' blades; there were many extra-wide fortes found on flattened hexagonal blades and I've seen some tapering into almost 'foil' like proportions.
Timing !!!
In regard to later horseman's swords, that hilt you illustrate Jim is what they fitted to the first (1687) batch of Shotley Bridge swords, distributed amongst the Jacobites and Catholics up here when the Germans first arrived with smuggled blades featuring the Passau Wolf AND the 'Shotle Bridg' script.