Prop planes cannot break the sound barrier. The faster you go the less thrust you get fropm the prop and the more drag. When diving props get to the point where the propellor is effectively a big airbrake on the front of the aircraft.
The only things that could, conceivably, have done it in WWII are the Me262, Me163, He162, Meteor Mk III, P-80 or the MXY-7 Ohka "Baka".
Personally, if it was done, I'd put my money on the Me262.