None of the examples you listed are "special forces." Special forces, as we think of them today, are trained for unconventional warfare. That was a distinction that didn't really exist in medieval warfare. The kind of things we might think of as special forces missions today, like raiding or doing reconnaissance behind enemy lines, were simply part of the standard tasks of the medieval army. They did not have designated units to cover these roles. A unit might be assembled to perform a particularly important task, like at Agincourt where the French picked some of the most experienced soldiers to perform a cavalry assault on the English flanks, but this wasn't a permanent arrangement. Medieval armies were not standing forces, but amalgamations of smaller groups that would be assembled for a specific campaign. No two armies would be exactly the same in terms of composition (although there would be plenty of soldiers fighting in repeated campaigns).

Mercenaries were sometimes hired to fill gaps or for particular roles, but they wouldn't be treated in a different way and couldn't be called special forces. A monarch whose kingdom was lacking in expert gunners might hire some Burgundian or German professionals to man the cannons. But neither they nor any of the other soldiers you mention were "special" outside of being competent professionals available relatively easily. The Swiss weren't being hired for unusual capabilities; they were being hired as highly competent regular infantrymen. Likewise, an Italian city hiring an English free company wasn't hiring them because the English are specially trained. Although some regions were notorious for mercenaries, mercenaries were available practically everywhere. There were French, Spanish, English, German, Burgundian, Hungarian, Italian, etc. professional soldiers all being hired across Europe.