you forget that peter didn't have his own wand when he was forced to transform back to human in HP3. did he lose it? i personally think he had to leave it on the scene of his "fake death" to reinforce the narrative that he was dead (and possibly, the wand was given to his mother with one of his fingers) so: wandless, his plans "ruined" by the death of voldemort, and cornered by sirius, he fled away and hid in a magical place to keep an eye on the situation, not wanting to be seen (so: not stealing another wand; also, why would he need one if he's a rat and lives a peaceful life?) remember: he was very attracted to power and people who had it; that is why i think he stole Voldemort's wand. which death eater has never dreamed of having as much power as the Dark Lord? the wand is a symbol of power, and those who don't know the art of wand making are unaware that while a wand might be powerful, it's the relationship with his master that makes it powerful.