I hate to break it to you, but the shimmy (I assume you mean wobble) may come back.
I don't remember having any wobble until my original tires(IRC), and my first replacement set (Pirelli Diablo)got some miles on them. I replaced the front last summer (Metzeler)thinking the wobble would go away. It didn't. 2000 miles later I put a new rear tire (Metzeler)on and the wobble went away.
I now have about 4000 miles on the front Metzeler and 2000 miles on the rear Metzeler and the wobble is creeping back. I am talking about a high speed wobble - above 50 mph - not the usual low speed wobble (32-25 mph coast down). I can't find any reason for it other than tire wear.
Enjoy that new bike ride while you have it. The scooter is wonderful when it rides so nice, isn't it? My wife just got a 2005 Majesty that has almost new Diablos on it, and the handling is natural feeling as you could ask for.