The varios State Troop weapons are not province specific.
IIRC Warmaster stated that spears are more common in the eastern provinces while halberds are more common in the central & western provinces. That's about the only difference you find in the grand view descriptions.
Swordsmen I think were originally thought as support and specialist troops, like in RW renaissance period, but because of the Shield rules gamers started to use them in big blocks. Also Citadel/GW had a large number of various sword&board adventurers, so needed to incorporate them in the original Warhammer Fantasy Battles. Surely you can find Swordsmen units in all the provinces. Just like you can find Greatswords - whether they are the 3rd-5th ed support unit or the 6th-8th ed guards unit.
There were some specifics about Handgunners or Crossbowmen in different parts of the Empire, or between the Empire and Tilea. And some ideas about Archers, who were or included Bergsjaeger and Forstjaeger - a natural difference between the mountainous and forested parts of the Empire.
Mordheim had different kind of Empire Mercenary bands, but the differences were not in weapon choices. All warbands could have Swordsmen, all warbands could pick whatever weapons.
You can do whatever you like with your minis.
Sellswords = mercenaries, which Marienburg employs, but there's that wordplay with 'sword' in there. But they could as well be 'sellhalberds' or Tilean 'sellcrossbows', it's just a metaphor.
-Z