No-Pest Vent, 4 Inch Soffit Vent Cover, Great for Bathroom or Dryer Vents, Patented Dual Door Design Prevents Birds and Back Drafts, Highest Efficiency Soffit Exhaust Vents on the Market (Onyx Black)

Not claiming it's the best way because it sure looks janky, but I found that mounting the fan directly to the back wall really amplified the vibration from the fan. To quiet it down I made a little stand out of pressure treated 2x4 and set it away from the sauna structure an inch or so, and connected ducting to a surface flange ( https://www.amazon.com/dp/B0DYYSKDCS "Duct Connector Flange 4 inch") that I screwed to the wall over the 4" hole. I mounted the fan with flow facing down, and put a soffit vent cover on the outlet to keep pests out: https://www.amazon.com/dp/B0FQW86D18 "4 Inch Soffit Vent Cover, Great for Bathroom or Dryer Vents"