The Imperial forces must keep their hands off, but they find that they can do much even so. Each sector is encouraged to be suspicious of its neighbors. Within each sector, economic and social classes are encouraged to wage a kind of war with each other. The result is that all over Trantor it is impossible for the people to take united action. Everywhere, the people would rather fight each other than make a common stand against the central tyranny and the Empire rules without having to exert force.
There is nothing your knife handlers can do in the way of rioting and demonstrating that will have any permanent effect as long as, in the extremity, there is an army equipped with kinetic, chemical, and neurological weapons that is willing to use them against your people. You can get all the downtrodden and even all the respectables on your side, but you must somehow win over the security forces and the Imperial army or at least seriously weaken their loyalty to the rulers.