Many years ago, (no age jokes, please), a friend was tinkering with a big B&S engine, maybe 12 or 15 hp. He came across an automobile 3 speed stick. With a bit of welding he built a crude frame, installed a motorcycle fork system for steering. He mounted the tranny across the frame with a pulley on the input shaft and a sprocket on th output. The pulley linked to another on the engine shaft and the sprocket to the axle. By squeezeing the clutch lever he depressed a belt tensioner just in front of the input shaft pulley. When he released it a heavy spring pulled it to tension the belt and engage the tranny. Worked real well but was hard on the hand due to the pull of the clutch release. He eventually swapped to a pedal actuated with linkage. A bit more complicated but the tension wheel was permitted even more spring power.
That was one flying, low horse, home made kart. So, yeah, it'll work and work well.