I'm coding a mechanic which allows a user to move around the surface of a sphere. The position on the sphere is currently stored as theta and phi, where theta is the angle between the z-axis and the xz projection of the current position (i.e. rotation about the y axis), and phi is the angle from the y-axis to the position. I explained that poorly, but it is essentially theta = yaw, phi = pitch

Vector3 position = new Vector3(0,0,1);
position.X = (float)Math.Sin(phi) * (float)Math.Sin(theta);
position.Y = (float)Math.Sin(phi) * (float)Math.Cos(theta);
position.Z = (float)Math.Cos(phi);
position *= r;

I believe this is accurate, however I could be wrong. I need to be able to move in an arbitrary pseudo two dimensional direction around the surface of a sphere at the origin of world space with radius r. For example, holding W should move around the sphere in an upwards direction relative to the orientation of the player.

I believe I should be using a Quaternion to represent the position/orientation on the sphere, but I can't think of the correct way of doing it. Spherical geometry is not my strong suit.

Essentially, I need to fill the following block:

public void Move(Direction dir)
{   
    switch (dir)
    {
        case Direction.Left:
            // update quaternion to rotate left
            break;
        case Direction.Right:   
            // update quaternion to rotate right
            break;
        case Direction.Up:
            // update quaternion to rotate upward
            break;
        case Direction.Down:
            // update quaternion to rotate downward
            break;
    }
}