Not to sure about a 2009 Seadoo's fogging, but all models I've ever worked with, come with a plug in the air box that you use to insert the tube for your fogging spray. You fog while the motor is running, just before shutting down.
Using 2 stroke oil? If that were the case, then we would not have to fog our 2 stroke motors at all, since our cylinders are coated with 2 stroke oil on a regular basis. I think you are mis-quoting. The dealers said you use the same fogging oil as they do in the 2 strokes, but it's not really a "2 stroke" oil. The fogging oil is more like a sprayable grease, that sticks to the cylinders over a long period of time. The reason you do it is to protect the cylinders from moisture build up. If you have un-protected cylinders, rust might be able to form on them.
I live in the deep south of the U.S. and really don't need to fog for Fall and Winter. I do start and run my motors once every couple weeks. I did have one motor that was a spare, I fogged it with spray on "Lithium" grease. Lithium is commonly used by mechanics when assembling a new motor to protect the surfaces from the elements. When you start the motor, it's washed and burned by the gas for combustion.