Don't get me wrong the left hand throttle to screw with people would be great. However, perhaps your looking at the problem the wrong way. Heres 2 different solutions followed by 1 question.
Perhaps the use of a Camelbak would allow you to enjoy hands free Latte sipping. I'm not sure how well they take hot liquids though.
You could handle bar mount you beverage with a motorcycle cup holder that swivels they are readily available. Add a piece of tubing and once again you can enjoy hands free Latte sipping.
Why do you have a moped? Is it to save $ in any way? if so perhaps not drinking that overly price beverage could be even better.
my 2 cents