I've swapped QT50 onto a towney frame.
Going from QT50 to PW50 you're gonna need to:
1) swap out the drive shaft assembies. From your QT50, use the rear shock, wheel, rear hub, and drive shaft. This will ensure you have the right final drive ratio and engine+wheel geometries fo the handling doesn't get any worse.
2) The wiring is almost certainly different, you may need to swap the stators cause PW50 doesn't have lights. Yamaha flywheels have a puller unlike most other mopeds, but they are easy to buy online.
3) throttle cables may be different. Use the PW50 throttle cable, caburetor and airbox.
4) a towney motor cannot be easily mounted on a QT50. Transmission parts for towny's are not availible. Towny has a different exhaust thas not compatible. Id stick with the one speed motors so you can fix/maintain it easily. (edited)