My partner wants to make a landsknecht getup for me, so of course I'm in the market for a new sword.

Thing is, there were a lot of swords floating around German-speaking lands in the 16th century, but some have become strongly associated with Landsknechts while others haven't. You have katzbalgers, rapiers, grosses messers, kriegsmessers, dussacks, swiss degen, complex hilted arming swords like the Munich town guard swords, and probably lots more. As far as I'm aware, 'landsknecht' was never an exclusive term for any one organization with enforced standards of equipment etc.

Question is, can we say any of the preceding swords are 'wrong' for a landsknecht on the basis of any compelling evidence? If you know of any good sources on this topic, please let me know.

I think they were mercs and employed in specific ways so I would imagine that there are certain weapons that are more appropriate than others. Of course, you mention some of the big ones - zweihanders, kreigsmessers, katzbalgers (and other s-guards - such as on daggers), daggers with rings, pikes, halberds, etc. Not sure about swiss daggers, dussacks, rapiers, and other complex hilted swords.

One place you might try looking is at some of the osprey books - they are pretty specifically targeted. I know not everybody likes them. But if you're not looking to get really academic about it, then I don't think they are going to tell you anything wrong. The illustrations and pictures are cool in them too.

https://www.ospreypublishing.com/ca/landsknechts-9780850452587/

https://www.ospreypublishing.com/ca/landsknecht-soldier-14861560-9781841762432/

The term Landsknecht wasn’t used in administrative texts, which often just used Knecht or Fußknecht. The definition appears to be a little fuzzy. It is certain, though, that a Landsknecht is a German mercenary and usually a foot soldier. The term is used in contrast to the Swiss Reisläufer. They may have been recruited from the Low Countries as far as I know. So, the definition of German in this case would include the Low Countries and Austria, but exclude the Swiss. I am not sure how much difference in equipment there was between the Reisläufer and the Landsknechts though.

Landsknechts are associated with Kaiser Maximillan I, and the term starts being used at the beginning of his reign and becomes archaic in the 17th century. I am not sure how different the equipment of conscripted troops were from mercenaries. I know that in the Late Middle Ages, the equipment was supposed to be the same. Conscripted troops, however, have been known to not have all the required equipment and might be more likely to have grandpa’s old sword. The better equipped Landsknechts came from the nobility or out of "good house". Because of their better equipment, they were paid better. There were also Landsknechts captains and different ranks. There is a question of if every fighting member of a Landsknecht army is a Landsknecht.

The Katzebalger is the most well known Landsknecht sword. This is possibly because it works well as a side weapon for a pikeman, or other long weapon. It seems to have also been used in historical iconography to differentiate the Landsknechts from the Swiss. There is also textual evidence that the Swiss did use Swiss dagger/degens and the Germans Katzbalgers. https://www.google.de/books/edition/The_landsknechts/8kmkDQAAQBAJ?hl=en&gbpv=1&dq=katzbalger&pg=PT37&printsec=frontcover https://www.google.de/books/edition/Gewalt_im_Mittelalter/qfQIK51neBIC?hl=en&gbpv=1&dq=katzbalger,&pg=PA47&printsec=frontcover

I think for any other sword besides a Katzbalger, one needs rather to look for evidence for it, rather than for evidence that it is wrong. It would very much depend on the type of Landsknecht and the time period. You mentioned the 16th century. The town guard swords are dated around 1600. Rapiers and sideswords are seen as civilian swords. Dussacks are more typical of Bohemia, but it is worth looking into, along with Messers, and medieval Longswords.

There are a lot of artworks depicting Landsknechts, although I am not sure they are all correctly labeled. Dürer has a few works with Landsknecht in the title, but the soldiers depicted don’t wear the typical Landsknecht clothing. Maybe it is an earlier style? They tend to have cruciform swords.

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Here are some other possible Landsknechts with not Katzbalger swords:
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