In my experience, some 2-stroke outboards smoke a lot until they are warmed up. Then it’s quite minimal. Keep in mind that there will probably be more unburnt fuel at startup because you either primed the motor (actually, it depends on the primer design if it will richen the fuel/air ratio or not, but that’s not the point) or gave it choke (or both) to start it. This gives it more gas, but not more spark to burn that gas.
Also, synthetic oil is known to burn cleanly in 2-strokes, so I would not listen to that dealer warning you about putting too much synthetic oil in your fuel mix. More oil is safer than less for these old 2-stroke outboards.
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