There are a lot of zero-turning-radius lawnmowers out there, most of them controlled by two big levers--one for each of the operator's hands. They could be controlled by a single joystick like most electric wheelchairs, that would only free up one hand. I propose converting both the hand controls to
foot controls, and freeing up both hands.
The foot controls could be two foot pedals, much like those already found in hydrostatic transmissions, or two spring-loaded levers long enough to require some leg motion to control them. There would be hand controls for the engine speed and the parking brake, and could even be a joystick as well.
There will be some time required to learn the skills of foot steering, but it has been done before. Most airplanes are steered on the ground by pedals, either just as brakes for each side of the aircraft, or by steering the nose- or tail-wheel.
The advantages of a foot-steering system should be appreciated by commercial mowers. The mower operator can carry a rack of lawn-care tools on the mower, and would be able to use a string-trimmer or a trash spike without dismounting. The homeowner who is not in such a hurry could carry a martini in one hand and a pipe in the other, or use a laptop computer to check stock prices or to order more fertilizer for his lawn.
Of course, there's something to be said for a parasol in one hand and a gold-lame' glove on the other, waving languidly to the populace, but I don't think I could carry that off.