Hi, I'm new.
Wasn't it mentioned that Harry wouldn't regret saving Wormtail at some point down the line? Perhaps that's why - when it comes to the crunch, Wormtail will spare Lupin as his debt to Harry (I hope so, anyway.)
I have a few theories about this, one being that JKR introduced the silver hand business as a distraction of sorts, so those well-versed in werewolf lore would inevitably think, "Oh my God, Remus is going to die!" when she might actually plan to have him survive the series. He's a good guy who's had a rough deal out of life - it would be nice to see him live and be lauded as a hero (and reinstated as DADA teacher after the war!)