I like it... I think that he picked up the wand, after he confronted Sirius (which was the next day I found in the book) and then turned into the rat again (so it was safely kept where McGonagalls robes go) and then used only once to kill Cedric, which is why he came out of the want too (remember, Voldie told Peter to kill him...)!
Naturally he couldn't ahve used it while he was with the Weasleys, since he was a rat, and it he changed back to Peter, he would ahve stood a big risk of getting caught (since there were what, 9 or so of them running round the house!!!)
So yeah, I like the theory!!!
