Just curious, why do you need to know the cox? To formulate some sort of equation for hand calculations? Remember that they are not very correct. Use them to get a feeling for which handles to pull in order to say increase gain or bandwidth.
And, in order to find parameters such as these, what about running a simulation instead and characterize the device that you need for your application? That enables you to also find the capacitance vs gate voltage, current, etc.