No Pump needed Use Charles' Gas Law
I agree you shouldn't need a vacuum pump. In a sealed environment as the outside air temperature decreases so to will the volume of air in the sealed environment. If simply cooling REHAB with dry ice doesn't decrease your air volume to meat your criteria then plum a preassure cooker in place of your air compressor. Remember the steam created will need to be vented to normal air as the preassure cooker comes up to temperature. Once the required temp is reached shut off the heat, close the vent to air and cool the preasure cooker. This will draw air out of REHAB to equalize the preassure between the two enclosed containers creating a vacuum in both the preassure cooker and REHAB.