Answer
The combined angular momentum stays the same. The angular speed of the turntable decreases.
Work Step by Step
The turntable and you may be considered as the system. The bearings are frictionless, so there is no net external torque. The angular momentum of the system is conserved.
As you walk toward the edge, you are moving mass away from the center, increasing the moment of inertia of the system. Angular momentum is conserved.
$$I_{old}\omega_{old}= I_{new}\omega_{new}$$
The moment of inertia increases, so the angular velocity decreases.
