You are ABSOLUTELY NOT INSANE.
Yes you will probably not go as fast, and you will not want to hit gators as hard. You also will really not want to go 2 off (or 4 off). But it will be a great learning experience and the Z should be more than able to handle it unless you have some other problems going on.
That being said, if you dont' feel safe doing it, I wouldn't risk your life / your car / other competitors.
On the plus side, rain will probably mean a lower turnout and more track time or less traffic for you.
Here is a video of one of my track days from last years in a thunderstorm on street tires. The track CMP is known to be very technical and although not "high speed" I was getting into triple digits. When it was raining heavily I did end up throwing on TCS.