Toyota Camry catalytic converter symptoms

My 2004 Camry with 125K miles makes a rattling noise from the right rear when started cold and driven for maybe 10 minutes then the noise seems mostly to go away. My local mechanic ran diagnostics and found no error codes. No check engine light is on. The spark plugs were replaced at 75K but not the ignition coils.

He removed the heat shield but that did not make a difference. Looking on line suggests that a loose honeycomb inside the converter could make a rattle noise.

Given this background, I wonder if the converter is responsible for ANOTHER problem where the engine runs rough and jerky at almost exactly 40mph and 60 mph. It’s not a shimmy or something felt through the steering wheel but an un-smooth running engine giving a herky-jerky feeling as you travel forward.
The mechanic did a test drive 40mph but did not experience the un-smooth problem.

Any suggestions are greatly apprciated.

I the mechanic willing to put the car on a lift overnight, then start it and listen for where the rattle comes from?
The cat converter won’t cause driveability problems unless it’s clogged.
As for the rough running I’m surprised you didn’t get the CEL with a misfire code.
Are the spark plugs OEM (Denso or NGK)?
I’d first get the MAF sensor and throttle body cleaned, fuel injectors cleaned and fuel filter changed (if it has one).
Then check fuel pressure and compression.

Thanks for the suggestions circuitsmith. I’ll have to get back with the mechanic looks like.