Let's forget emissions for a second... is the cat needed? Without the added back pressure are there issues? What happens if the matrix inside the catalytic converter is removed?

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'91 240 wagon, '89 240 wagon, '90 740 sedan, '92 740 wagon

Exhaust volume (sound level) may be bit higher without cat or matrix. If the car has an O2 after the cat you'll likely light a check engine light/set a code without cat or matix. Otherwise shouldn't matter. Millions of cars out there that once had cats running around catless.
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82 242 6.2L coming...; '15 Honda Fit; '16 Subie X-Trek

I just changed my header pipe and cat. The cat that I replaced was empty and had the o2 sensor screwed into it.

That's what I was thinking, thanks guys!
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'91 240 wagon, '89 240 wagon, '90 740 sedan, '92 740 wagon

Another, more reliable solution would be to have an exhaust shop fabricate an exhaust pipe with flange to seal and secure to the header pipe output flange.

The exhaust shop cuts and hole and welds a Oxy2 sensor bung to the pipe.

The pipe is shaped to maintain alignment of the exhaust. Also secure to the front resonator (front muffler).

A dated catalytic converter shell may be rusty or remaining ceramic pieces may work back to the one of the two mufflers.

Probably be fine though. Also be sure the integrity of the bracket hanger set-up that secure to the end of the header pipe. Sort of important support point along the 240 exhaust.

On a whim, you may want to test the exhaust gases after your catalytic converter removal. You may find they are rather 'clean' even without catalytic converter scrubbing. (Though NOx will be higher.)

Happy Sat-Your-Day.

Earl Grey Tea Bastard.
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