Your general idea is correct. Your fingers apply a force which can be translated to a moment at the rotation axis. The reaction forces applied by the object to be cut must generate an equal moment at the axis. If the necessary reaction forces are greater than the object's shear resistance forces, then the object is sheared through.
For this reason, it is best to place the object as close to the axis as possible, so that the forces required to balance the moment are maximized. Too close, however (at which point the angle between the blades becomes greater than 90 degrees), and you run into the problem that the forces start becoming primarily horizontal (pushing the object out of the scissors) as opposed to vertical (cutting through the object).
This is because the blade's force is applied perpendicular to the blade, so the greater the angle between the blades, the greater the horizontal component of the force becomes. This component is useless since it does not serve to cut through the object, but instead simply tries to force the object out of the scissors. Only the vertical component actually shears the object. This is because the horizontal components of both blades point in the same direction, while the vertical components point in opposite directions.