I don't know about your engine, but many engines will almost totally close off the fuel line in the carb if you pull the throttle closed. Try making sure you can totally close the throttle barrel, and leave the throttle set there after the engine is stopped. That's been enough for me in the past.

Guys that run pressure tanks sometimes use a clamp on the fuel line. I've seen some hooked to the throttle servo so that the fuel line is pinched when the throttle is pulled all the way off. But that seems a bit extreme for your situation.