Do I need to replace my O2S3 when replacing my catalytic converter?

The catalytic converter that I will be replacing has an O2 sensor downside of the cat.

You will need to have a sensor down stream yes.
No as long as you don't damage the old one you don't need to buy a new one

Generally O2 sensors unscrew from the fumes, this implies you ought not need to supplant it (unless it is flawed) and it will screw into the new feline. con. once fitted.