"Normally, you'd have to go into the grave of one of your ancestors and retrieve a sworwd that had been buried with them, but that's not really an option here."

Here as in "here at the inn", but also here as in "in this particular situation". Even if they weren't trapped here, Thor somehow doubted that his father had been buried with a sword for this particular purpose. And with Asgard gone, he couldn't exactly retrieve a weapon from Bor's grave for this purpose.

"Normally, you'd wear it during the ceremony, then gift it to your partner. There's this whole wring ceremony, too, where you have the rings balanced on the hilt of the sword." Thor waves a hand. "All standard stuff. The best part of the sword thing is when they stab the ceiling."