IF you run an expansion chamber, then the smaller the exit (stinger) the MORE power you get....the extra backpressure results in extra "supercharging" effect from the tuned pipe. The engine will also run hotter, so there is a limit to how far this can be pushed. My point is that quiet operation often goes hand in hand with increased backpressure, and with a tuned pipe, you needn't trade performance to get it.
That said, a good deal of the noise from any aircooled engine is not coming from the exhaust. It is comming from the cooling fins, sounding boar....er I mean clutch cover, and so forth. This tends to be higher frequency stuff, and fairly obnoxious....a good deal of the "ring" in the "ringdingdingding" sound dirt bikes are known for.
Stuffing some polymer blocks between the cooling fins to damp vibration is one of the tricks used to help quiet air cooled engines.