Well that is sucky. I wouldn't recommend going to a Hardware Store to try and furnish a solution, sure the spring might fit, but what's the right tension in the spring? That's something that is factory tested to a "T". I would hate for you to do that and then SPROING, your friggen heatsink/fan flies off mid game.
IMO, try calling gigabyte and seeing if you can order that part. Even if it's a few bucks, better than buying a new card and better than wondering if an outside solution is safe.