I do not have a strong understanding of grounding, but it seems to me
that attaching GND to the cathode end would allow the transient to
flow into IC pins (via GND) and thus provide no protection.
The idea of ESD circuits is you want the current from the ESD spike to be shunted away from sensitive electronics. Typically this is done by connecting the diodes to a chassis ground or shield, so the pathway will not be through the ground but out through another pathway and back to the source (usually earth ground which is 0V). If your design doesn't have a chassis ground, then shunt it to the next best place, ask yourself, where do I want these currents to go once they have passed through the diode. With careful PCB planning (like locating a ground connector close to the TVS diodes) can direct currents away from the electronics.
Would it be correct to attach a metallic shield to the board at one
point and and route the transient there, or something else I am
That would be one option, one way I've done it is have a separate chassis ground for the shields of connectors and protected inputs, which is connected via fastener to chassis ground.