Joshua

As I just pointed out the Hobbits got their Barrow Blades( and yes they had them in addition to the Noldor Daggers) from Arigorn at Weathertop instead of from Tom like in the books but it's not a plot hole as presumabl Arigorn found them near by at Weathertop and as that had been a great watch tower of Arnor during the days of its fight with Angmar such blades were just as likely to be found there as in the Barrow Downs as they were designed to fight the Barrow Wights and other similar creatures that the Witch King sent against them. The swords were designed with magic that effectively seperated a Wraith from the spell that held them in the Wraith world and under Sauron and the Witch Kings power so for a brief minuet they were mortal again and could be then killed.

The Whitch king was not stabbed with a Noldor Dagger and that's obvious he was stabbed with a Barrow blade the only difference is they are given those blades by Arigorn in the beginning instead of Tom Bombadil when they are at Weathertop. That's the sword he uses.