Knowing how to build a wing isn't going to be of much help when your number 3 engine is up in flames
Honestly though, at least in the U.S. most airlines *usually* don't care what degree you have, as long as you have one. You could have a PHD
in bovine psychology and they'd still hire you.
I'd say in your case just pick a degree you'd be interested in and fly on the side.
From what I've heard demand for pilots should decrease slightly within the ten next years (we're at a peak right now), but there should be plenty of positions still by the time you get all your training done.
Right now I'm at ERAU and in my last year here. I'm pretty much done with flight training and I'll be getting my degree in aeronautical science with a minor in aviation weather. I've been really happy here and you might want to consider a reputable school like ERAU, UND, or Purdue, but bear in mind this route is not for everybody.
It's just one of the myriad of options out there.