Scooterg, while the T5 is a good engine, standard cranks and cylinder kits can be/ are expensive and the choice of tuning kits are somewhat limited (though a few new kits have came out recently) and keeping in mind your frame is a genuine 200 cc frame, if I were you, I'd get a p200 engine as genuine Px200 scooters can only get rarer and more valuable imho 😉.
Genuine honest answer is ive no idea. There isn't many people who would think to change the engine number on the logbook if ther were swapping like for like. I know I don't get on well with them, but wouldn't the Vespa club know?
My experience with these guys is they are a bunch of stuck up c**k lords who will not help anyone with anything, and will not have a problem stabbing you in the back. To the dvla. w*nkers. But, there are some people who's faces fit.....,