I disagree with your interpretation of Joseph Swetnam’s book. You said that Joseph Swetnam wrote that a long sword was a two-handed sword. Here are some quotes from a transcription.
"Scholler. What be the sixe weapons which you would have me to learne.
Master. The first and two principall weapons are the rapier and dagger, and the staffe, the other fowre are the back sword, the single Rapier, the long sword and dagger, and the short sword and dagger, but with the two former weapons thou maist encounter by skill with any man in the world, the rapier and dagger against any weapon of the same length, at single hand and with staffe against any two handed weapon, as against the welch hooke, two hand sword, the Halberd, Partisan, and Glove, or any other weapon of the like advantage : but provided alwayes thou must be sure armed with skill at those two especially: and with all the rest if thou canst, for then maist thou bee the bolder to encounter with any man at any of the other, if thy enemy can doe with his weapon, which if thou hast no skill in, it will seeme the more fearefull unto thee."
It would make most sense to speak of the long sword and dagger if the long sword was a long single-handed sword, not a two-handed sword. The two handed sword is mentioned separately.
“In describing of this weapon I shall account the time ill spent, yet because Short swords are in use and worne of many that would leave them off if that they knew what an idle weapon it were, I meane to encounter against a long Sword and Dagger, or a long Rapier and Dagger, so small is their Iudgement, but onely this, many of them will say it is a better weapon then any of the two foresaid weapons are, but in my monde they may aswell say that chalke is cheese because they are both white, for I have had much triall and great practice with the short sword, yet could never find, nor never wilbe perswaded but that a Rapier foure foote long or longer, hath such great oddes, that I never meane to arme my selfe with a short sword against it; for in my minde and by experience I speake it, there is small skill to be learned with the short sword to encounter as aforesaid, but onely resolution and courage.”
Here we have “a long Sword and Dagger, or a long Rapier and Dagger”.
“He that is valiant and venturous, runneth in, breaking distance, if hee escape both in his going in, and in his comming out unhurt; for a man skilful, in my minde it is as a man would say chance-medly, for if I have the Rapier and Dagger, I will hazard both games, and against any man that holdeth the short sword to be a better weapon, although that George Giller hath most highly commended that short sword & dagger, yet one Swallow maketh not a Summer, nor two Woodcocks a Winter, if a thousand more were of his opinion, yet without all doubt there is a great deale more danger then at Rapier and Dagger; or he that fighteth with a short sword must adventure in pell mell without feare or wit, but have seldome heard or seene any fight with short sword and dagger, although they be each weaponed alike, but one or both commeth most grievous wounded: my reason is the distance is so narrow that a man can hardly observe it, except thy have been both practioners a long time before hand, for if a man practice continually long sword or long Rapier, yet upon such a Challenge goeth into the field with a short sword, then the daunger is greatest of all: aske Augustin Badger, who speaketh highly in praise and commendation of the short sword, for hee hath tried that weapon in the field so often, and made as many tall fraies as any man that ever I heard of or knew since my time, yet hee will say that he never fought in all his life: but was sore and dangerously hurt.”
Here we have “for if a man practice continually long sword or long Rapier”
"A guard for the short sword and dagger to encounter
against the long Rapier and Dagger, or else the
long sword and Dagger."
"Keepe your sword hilt so high as your head or higher at the point, hanging slope-wayes down-wards a little wide of your left side, looking under your sword arme with both your eyes, and withall all put out your sword hand as far from your body as you can, I meane towards your enemy, and your dagger downe by your side, as if you meant not to use him at all, according to this picture."
Here we have a picture of a long rapier, or else a long sword.
Below is an extract from where it lists the different weapons.
"The two hand Sword.
The Back-sword.
Sword and Dagger.
Sword and Buckler.
Short Sword and Dag- Ger.
The short Sword and Gantlet.
The Bastard Sword, the Which Sword is some- thing shorter then a long Sword, and yet longer then a Short- sword."
Here we have a sword called a two hand sword.
I believe that if the transcription I used is correct, this is a very good case for a two handed sword having been called a “two hand sword”, and for the sword called a “long sword” being a long single-handed sword that can be paired with a dagger, similar to a rapier.
I would like to add to the commentary of George Silver’s works.
"WHEREIN IS PROVED THE TRVE grounds of Fight to be in the ſhort auncient weapons, and that the ſhort Sword hath aduantage of the long Sword or long Rapier. And the weakeneſſe and imperfection of the Rapier-fights diſplayed. Together with an Admonition to the noble, ancient, victorious, valiant, and moſt braue nationof Engliſhmen, to beware of falſe teachers of Defence, and how they forſake their owne naturall fights : with a briefe commendation of the noble ſcience or exerciſing of Armes.
By George Siluer Gentleman.
LONDON,
Printed for Edvvard Blount.
1 5 9 9."
This is at the beginning of his Paradoxes of Defence.
_"The two hand Sword, hath the vantage againſt the Sword and Target, the _
Sword and Buckler, the Sword and Dagger, or Rapier and Poiniard."
This is in the bit where he wrote which weapons had the advantage over which.
From this we can see that to George Silver, the two handed sword had the advantage over one handed swords, and the short sword over the long sword or rapier.
MS Harley 3542 (early to mid 15th century) calls the two handed sword, simply, the two hand sword.
Cotton MS Titus A xxv (15th century?) also calls it a two hand sword.
#PS
The name of this thread is “Short Sword”, so I will say something on the subject. Joseph Swetnam and George Silver’s books use the term “short sword” for a sort of one-handed sword, not one-handed swords in general, which is the common usage in modern English too.