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You need the O2 sensor. If you get rid of the cat, you can either get rid of the tubes or just leave them. they dont do anything important if the cat is not there
If you have an O2, you need it, as it feeds information to the cpu that controls the mixture settings on the engine. Also, depending on where you live in TX, you might have to go through emissions testing to get your license plate, if the O2 sensor is gone, it will not pass.
Can I just weld in a threaded collar in the pipe for the O2 sensor and let the air tubes dangle? Its obvious the O2 sensor is important, but what is the function of the tubes in stock exhaust form and what happens if they aren't in a cat?
P.S, they don't do emissions testing here. I've passed inspection driving a straight piped Cummins.