That's not really that expensive, to be honest. You are shipping it across the world to have it professionally repaired.
But honestly, while it's scary to take your Deck apart, they made it pretty cheap to repair if you want to do it yourself. The button in question is less than US$10 for a pair, so you can replace both while you're in there. And while you're at it, you might as well upgrade the joysticks to those fancy ones the enthusiasts are always going on about.