So you will pay in euros.
And then pay the conversion rate that your CC company pick!!!
In all of this, HMRC know that most folks will either pay the APD - or not go. Those that will avoid it by making a long stopover are very few. For the most part, the extra hassle is only worth it if you have a good reason to stop at the stopover and visit the place or people there.
When I'm booking, I ignore the APD, along with everything else. It's just the bottom line that counts. If I cannot afford the flight that I want, on the routing, the carrier and the aircraft that I want? Then I won't go (unless it's life or death)