No no no no no... FFS NO!
If you ran the exhaust from an RC32/60 into my vacuum pump, I'd beat you to death with a cricket bat. See the rocket motor instructions:
NOTE: Perform RMS-RC motor cleanup as soon as possible after motor firing. Propellant and delay residues become difficult to remove 24 hours after motor firing. These residues can lead to corrosion of the metal parts
Put a safety interlock on that valve; valve open, firing circuit open. Throw the steel outer pipe away as it's unnecessary and heavy. Use a rectangular plywood box for the outer shell with thick expanded foam insulation between it and the vacuum chamber. Since the rocket engine is only 32mm in diameter, use s piece of four inch (100mm) copper pipe for the chamber. Braze the vacuum exhaust line into the side of the pipe.
You're going to need a second line into the chamber for your temperature sensor and the two ignition wires. I would suggest using half inch (1cm) copper pipe for this. Make it a short piece with a female threaded pipe fitting on the end. Use a second short piece with a male fitting leading to an expansion fitting to 3/4 inch pipe. Plug the 3/4 fitting where it narrows with a piece of balsa wood drilled with holes just big enough to take the wires. Fill the rest of the fitting with Apiezon vacuum wax. This will give you a reusable high vacuum sensor port at a not too horrible expense. If you use teflon insulated wires you should be able to heat the fitting up enough to melt the wax with no problems.
Final safety thought - be SURE that it's IMPOSSIBLE for pressure to build up inside the dry ice chamber. Big holes that can't possibly ice up. You might use vacuum grease at the top seal as well as rubber (silicone is better).