I have a few Fisher Space Pens, specifically the
Stowaway model which is the perfect wallet pen. I get the version with the clip which prevents it from rolling off the tray table. This pen is extremely slim, small and lightweight and I always have one in the change pocket of my wallet, one in my seat-bag. Sometimes I have one in the organizing panel of my carry-on. Being so small and thin, this pen is not particularly comfortable in the hand but it is 100% dependable. The only complaint about this pen is that it's not good for anything where you need to push hard when writing as the refill is only held in by a tiny rubber stopper at the end of the barrel. The Fisher Space Backpacker Pen has a screw on back but is much larger.
$10 for a ballpoint pen?
I find free hotel pens work just as well, and if they get lost, no big deal.