Compare the blades of Schiavone and Claymores: both are typically about 1m in length, and some of both are longer.
While the Claymore blades weigh over 2 kg, Schiavona blades weigh a little over 1 kg. Both are double edged, have points and are balanced for striking. While the points of Claymores might have been used only in very specific fencing maneuvers, there are Schiavone which taper out in small dagger blades, to make thrusting with them at range more efficient. So the Schiavona is indeed the early, Renaissance, model of a basket hilt cut-and-thrust sword.
The light, large blade of the Schiavona and other such cut-and-thrust swords require blade smith technology beyond the medieval one, but they do not require specific fencing techniques.
Having a blade light enough to comfortable wield in one hand while maneuvering a horse with the other, and at the same time long enough to provide the reach needed for cavalrymen, made these swords and their descendents the weapon of choice for many heavy cavalry.
Note, that heavy cavalry at this time was often still really heavily armored. It included the gens-d'armes, e. g. from the battle of Pavia, and the Polish Husaria, e. g, from the battle of the Kahlenberg. The latter had their own cavalry sword, the very long stabbing Koncerz developed from the cut-and-thust sword. Both relied on lance charges in formation, but due to the problems of the lance with recovery and follow up charges they needed wieldier weapons as well. Less prestigious heavy cavalry units gave up their lances earlier, and afterwards relied on the cut-and-thust sword as their main weapon before some switched to pistols.
Now think of a covenant and a magus making blades lighter, thereby making schiavone, maybe without basket hilts, well before their time. The typical grog or sergeant should easily adapt to their larger range, shouldn't he? Certainly faster than a magus adapts to finger twiddling in a gauntlet while striking!
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