Hi Jim,
As you can see, when it comes to storing outboards, snowmobiles, motorcycles, ATV's, etc. you're going to get a variety of methods and opinions on the "right" way to
do it. All you can do is pick the one you want to go with, and most likely you'll never have a problem. For me, I used to do as has been suggested by running my outboard at a slightly higher than low idle and spraying bursts of fogging oil thru the carb intake until the engine ran the fuel out of the carb. Always worked great.
In the last several years I make it even easier on myself. I just run the motor at a slightly high idle until the fuel runs out of the carb and it stalls. I then pull the spark plugs and spray liberal amounts of fogging oil in both cylinders, turn the motor over by hand a few times, and spray a bit more fogging oil in the cylinders. I then clean and check the gap on the plugs, or replace them if they've been in there a while, put them back in, drain the lower unit, and put it to bed. In the spring I put new oil in the lower unit, grease the grease zerks, and I'm good to go. I discovered that on every two-stroke engine I have ever torn down internally, even after it had been run dry of gas, that the bearings were always still very oily. I have since not worried about getting the fogging oil into the bearings, and find it more convenient to spray directly into the cylinders and do the aforementioned spark plug service at the same time. And now for the magical final words: "I've never had a problem when doing it this way."