Well, stratovolcanoes like Uturuncu are generally caused by the presence of a subduction zone. The nastiest volcanoes are linked to plate tectonics. There's hot spots too, in which the mantle violently penetrates the crust, but after making its initial thrust the mantle doesn't have much stamina unless aroused by the proximity of a cleft. I imagine we can tolerate the continued activity of shield volcanoes.

So let's get rid of the plates. What good have they ever done for us? They're responsible for earthquakes, volcanoes, and Australian wildlife, the bastards. Anyway, it may be difficult to actually put the Earth's crust back in one piece now that it's all broken up, so why don't we time travel back to near the formation of the planet and put a stop to all this tectonic business before it started.

For plates to form, the crust of a planet requires areas of weakness. On Earth, it's believed that these areas of weakness were created by the interaction of silica and water. Water is probably the easier of the two to do away with, though how exactly how that would be done is hard to say, due to our limited understanding of the Earth's formative years.

If you subscribe to the giant impact hypothesis (that a collision with another protoplanet caused the formation of the Moon), averting that may achieve our goal, as it has been theorized that material vaporized by the impact generated a high-pressure CO2 atmosphere which prevented the Earth's water from evaporating away into space. It has also been theorized that much of Earth's water may be of extraterrestrial origin, so putting an impenetrable force field around the young Earth to shield it from any and all collisions is a good bet.

Should we succeed, Earth's oceans will have been severely diminished or perhaps not exist at all, significant tectonism will not occur, and as a side effect of the reduction of surface water it is likely life would have never originated on the planet. A small price to pay for avoiding the threat of a supervolcano, in my opinion.