DOC
Fear not the spinner has far more to do with the look of speed than any real benefit to the ingestion of cooling air.
The air around the base of a prop rotating at 2500rpm or so is to say the least pretty disturbed and won't be much helped into the cooling intakes by the spinner.
Take a look at the older machines (Austers, Cessna 120 etc) - no spinner or a very small one at best.
Trust what the engineers tell you - they just might be telling you the truth......