Ask yourself: If this had been your plane and your passengers, would you have flown it? If not. Be at peace with your decision.

Of course, as a PP, you have a big advantage over the airline guys. You know that, if you cancel a flight for a reason like this, you will still have a job in the morning, you won't suddenly be out in the job market with few transferable skills and crushing debts from flight academies.

I'll bet the crew was thinking, "I wish that was me." as they watched you walk away.
--
Roger Long