What sled is the Ski Doo engine out of? Fan cooled, or a liquid? Here's my thoughts on it-
If it is an FC, it is possible to overheat easily, since the engine is designed for winter. If LC, where is the radiator going to go? You'd need a different radiator, since it would be a long radiator that is in the tunnel, and it wouldn't work out too well for swapping into a scooter. If it is an LC, my suggestion would be to buy some used radiators off a dirt bike of similar size (450, 500, 600, etc), and use air scoops with them.
Another issue would be the frame. It'd have to be beefed up to handle the torque, and made larger to accept the large engine.
One more issue would be the clutches. It'd be a pretty big thing hanging off the back when that's done.

My suggestion-
Get an old street bike or enduro engine. Anything is bigger than a scooter.

For kicks, find at least a 250. It'd need to be liquid cooled, since there isn't much airflow where it would be located.
With a motorcycle engine, it'd be easier to transplant, since the transmission is contained in the engine, and it wouldn't be as tough to make work. For a real thrill, get an old KX 500, CR 500, or RM 500 2 stroke race bike engine.
