On the main control box, you can only set the minimum and maximum speeds ie the speed range over which the speed control will operate, for example, minimum 500 rpm, maximum 2000 rpm or 2000 rpm to 3000 rpm etc. You can also set direction of rotation.
The simple answer to replacing the speed control box is no.
The long answer is yes, if you are competent with electronics and are prepared to modify the speed controller within the speed control box. You will need to determine from the speed controller what signal voltages define the motor start and and maximum speed of the motor. Knowing that you can replace the Hall transducer with a potentiometer.
Say for example these voltages were between 2.2v for motor off and 4.8v for motor max, then you will need to construct a voltage divider with potentiometer, or a two divider voltage clamp with potentiometer to replace the Hall switch.
You will need to make sure your ‘low voltage’ circuitry is well isolated from anything you may touch and anything metallic as it will be at high potential with respect to ground (ie possibly mains voltage or greater). I suggest you do not go delving around in the main control box unless you are comfortable working with high voltages.