It's not feasible, and even if it were, it would be a very bad idea.
Compare with Yucca Mountain, which was selected because it is remote, arid, and geologically stable. The latter two characteristics are essential so as to avoid problems with corrosion and earthquakes exposing the hazardous waste to the environment. The remoteness provides a contingency in case of exposure. Those ocean trenches are remote, but they are anything but arid and geologically stable. The immense pressure and salty water is a perfect environment for corrosion, and those subduction zones are the sites of the most intense earthquakes on the planet. Sans an unobtanium barrel, the waste will be exposed to the environment in short order, well before subduction draws the materials downward.