You are presupposing the falsity of selective texts as it suites a secular view.
I did not use the term 'false'.
To be exact, I came down on the side of Jesus's precognition of his own death being historically plausible, after first considering the possibility that it might not be (as a number of scholars do argue, nonetheless).
More to the point, it doesn't make chronological sense for the μάχαιρα in question to have been for Passover. Jesus tells them to buy μάχαιρα in verse 36, but they had prepared the Passover back in verse 13! Thus the analysis you posit is simply incorrect.
Your own reference from Strong's concordance substantiates that a
machaira was
properly speaking a "
slaughter-knife", which is to say a butcher's knife intended for the purpose of slaughtering and cutting up animals for a meal.
In Homer's
Iliad, to take the earliest usage in ancient Greek literature that comes to my mind, it always refers to a domestic, sacrificial knife in the context of ritual slaughter and cooking of an animal. Indeed, at one point during the epic Trygaeus instructs his slave to "
take up the sacrificial knife [machaira] and slaughter the sheep like a mageiros" (lines 1016-18), which refers to a professional butcher whose occupation is actually derived from the word
machaira.
In the Book of Revelation, we find verses where the unambiguous
rhompaia is used in precise reference to a battle-sword. If the Evangelists had made use of such an unanimously martial word, we wouldn't be having this discussion! The context determines whether
machaira might mean something more than its traditional usage and in our situation we have Jews celebrating the Passover (involving ritual slaughter of a lamb) which is akin to its ritualistic deployment in Gen. 22.6 LXX where Abraham is about to slaughter his son Isaac with a sacrificial knife.
The onus, in this context, is upon the given interpreter to prove the circumstances warrant reading more into the plain meaning of
machaira and I honestly don't see persuasive backing for it, because it is logical that the disciples - like every other group of male Jews at that time - would have been in possession of sacrificial knives for the meal (as, indeed, they would have used in their daily travels for gutting fish, since it was a multi-purpose tool) and that Jesus during the Last Supper would have told them to carry such an essential tool with them.
The primary purpose of a
machaira was to "divide", to carve up animals into parts for eating or ritual sacrifice, which makes it ideal for Jesus's metaphor in Matthew 10:35 which is about family division over the truth of the gospel.
I read Luke 22:35-28 as Jesus simply telling his disciples to be prepared for the journey ahead and take with them their appropriate tools, including the
machaira they had just used to prepare the Passover. In each account, a disciple (Peter in John) then wrongfully uses the knife to fight back in protection of Jesus, or indeed cut a man's ear off, to which Jesus subsequently reprimands him by stressing (again) a non-violent approach and putting a stop to any violent means.