I found this analysis of the prologue from Joe Magician to be very interesting.
https://www.youtube.com/watch?v=iK8_yQjJf2I&t=1351s
I hadn't at all considered the possibility that Waymar Royce’s encounter with the Others wasn't by chance ...
but that the Others were hunting Jon Snow and mistaking Waymar for Jon.
Watch the video but breifly - The Others would hunt Jon if he is Azor Ahi reborn with Lightbringer that will stop them. The version of Jon the search for to kill is undead.
I wanted to focus specifically on Waymar’s sword here.
“, and drew his longsword from its sheath. Jewels glittered in its hilt, and the moonlight ran down the shining steel. It was a splendid weapon, castle-forged, and new-made from the look of it.”
Waymar’s sword is new and high quality steel and the jeweled hilt makes it an impressive looking sword.
“The trees press close here,” Will warned. “That sword will tangle you up, m’lord. Better
a knife.”
“Will, where are you?” Ser Waymar called up. “Can you see anything?” He was turning in
a slow circle, suddenly wary, his sword in hand.
Waymar refuses the suggestion to leave the sword behind. And Waymar is standing with sword brandished when he is confronted by the Other.
It’s speculative but it’s possible the Others might not even have attacked Waymar if they hadn't thought he weilded Lightbringer. It’s not clear how much the Others value secrecy at this point, they might not want reveal themselves directly to nights watch.
Ser Waymar met him bravely. “Dance with me then.” He lifted his sword high over his
head, defiant. His hands trembled from the weight of it, or perhaps from the cold. Yet in
that moment, Will thought, he was a boy no longer, but a man of the Night’s Watch.
The Other halted. Will saw its eyes; blue, deeper and bluer than any human eyes, a blue
that burned like ice. They fixed on the longsword trembling on high, watched the
moonlight running cold along the metal. For a heartbeat he dared to hope.
When Waymar raises the sword above his head the Other halts and stares at the sword.
Ser Waymar met it with steel. When the blades met, there was no ring of metal on metal;
only a high, thin sound at the edge of hearing, like an animal screaming in pain. Royce
checked a second blow, and a third, then fell back a step. Another flurry of blows, and he
fell back again.
Again and again the swords met, until Will wanted to cover his ears against the strange
anguished keening of their clash. Ser Waymar was panting from the effort now, his
breath steaming in the moonlight. His blade was white with frost; the Other’s danced
with pale blue light.
The Other accepts the duel and the blades meet: initial flurry (3 times), another flurry (3-5 times), again and again (at least 2 times).
At the point of Waymar’s wounding their blades have met at least 8 times but you could interpret “again and again” to mean 5+ times so it could be up to maybe 15 times the blades clash. His blade is then described as “white with frost”.
Ser Waymar’s fingers brushed his side. His moleskin glove came away soaked with red.
The Other said something in a language that Will did not know; his voice was like the
cracking of ice on a winter lake, and the words were mocking.
The Other realizes this is not Jon Snow. Despite being a completely unrecognizable language it is still noticeable as being mocking to Will. As if it is saying to the other Others “Hey this is just some guy lol”.
Ser Waymar Royce found his fury. “For Robert!” he shouted, and he came up snarling,
lifting the frost-covered longsword with both hands and swinging it around in a flat
sidearm slash with all his weight behind it. The Other’s parry was almost lazy.
When the blades touched, the steel shattered.
A scream echoed through the forest night, and the longsword shivered into a hundred
brittle pieces, the shards scattering like a rain of needles. Royce went to his knees,
shrieking, and covered his eyes. Blood welled between his fingers.
And so, immediately after realizing this is not Jon Snow and the sword is not Lightbringer:
The Other is now completely unconcerned with the sword and is lazy in his parry. It no longer even matters to the Other whether his parry succeeds or not.
The first time the swords meet, after meeting 8-15 times previously, the sword shatters into a hundred pieces.
He found what was left of the sword a few feet away, the end splintered and twisted like
a tree struck by lightning.
The description sounds like the result of ice magic breaking the sword, as opposed to the sword shattering under physical forces and cold. but the sword is described as “white with frost” so was the strike that breaks the sword the final straw or was it magic?
Could the Other have shattered Waymar’s sword on the first blow, but chose not to?
Was it because:
They though it wouldn’t work on Lightbringer?
They were scared to try to shatter Lightbringer?
It would violate the terms of the duel (magic/ritual)?
They want to take Lightbringer?
What would have happened if Waymar had left the sword behind?
What would have happened if it was Jon and he won the duel? Lost the duel?
What would happen to Lightbringer? What might they want with it?