A cat shouldn't get hot enough to cause interior damage unless it was blocked, bad, or installed improperly.  That said, runnning a straight pipe shouldn't create a noticeable loss of backpressure or torque.  It is illegal, however, and if there are emissions inspections where you live, you'll definitely need one. 

No emissons here. I just dont want to loos torque

I doubt you'll notice any decrease in performance with a straight pipe.

sounds good psu

You may want to check to see if your carburetor is running to rich. A rich condition will overheat the catalytic converter. Also to much spark timing will cause the exhaust temps to rise excessively.

Is there a heat shield between the cat and the underside?

I wonder that meself...with the metal floor pan, and no heat shield, I would imagine it do get hot there!

A rich condition, as Darryl pointed out, will overheat the cat, as well as a problem with the AIR system...perhaps the AIR ain't working?

Doin burn-outs, were ya?

When they were testing the cat systems way back when, before the '75 cars came out, Zora actually burned a car to the ground from overheating the cat! He was coasting down a hill, engine running, and the raw fuel in the cat ignited...ooooops!

If it was me, I would eliminate the cat.  To me the less "junk" constricting the exhaust the better. But would do so only if you don't have to smog.  What about if and when the vehicle changes ownership? Here in CA, sometimes you have to smog with the new owner.  By the way, real good looking vette you have from pic.

I was just running up and down the street. I was not spinning the tires. I have no heat shield. So off it will goooooooooooooo