Sally, is there a specific reason that you are going to want that much cash on your trip? The reason I ask is that most of Europe has pretty much gone fairly cashless. You will find most of your transactions will be by credit or debit card and many places prefer this to cash.
Unless there is a specific cost that you know of where the vendor will only accept large amounts of cash, I think that getting $200 at a time will be more than enough for your needs.
I would encourage you to think about using a debit card vs. a credit card for cash withdrawals at an atm. A credit card will start an immediate interest charge on a cash withdrawal at extremely high interest rates, while simply charging an expense to a credit card will not. Debit cards will not cause you to be charged interest.
If you feel that exchanging at the airport is your best option still, I don't know that it will really matter. Simply go to the exchange, pay the fee, and go on and enjoy your trip.