I don't think that's it at all (although it is a nice theory). Peter Pettigrew did change himself to a rat, just after he cut off his finger and made that big explosion that got Sirius locked up. That's how he escaped. Of course, he had to leave his wand behind, because rats can't carry wands. So he had to stay a rat because nobody could change him back. And nobody knew he was an animagus, because he was unregistered, so nobody knew to change him back anyway. And he lived a great old life in the Burrow, so why would he want to leave that life? So he didn't change back into human form until Sirius (or Remus, I can't remember which one) changed him back in the Shrieking Shack.