What dragon? There are no dragons in my character's games. You never have to see one in this game if you do not want to. Never deliver the dragonstone of bleak falls barrow to Farengar, and you will never see a dragon. Simple as that. In fact, you can just ignore the rest of main quest leading up to that as well.
This. On two of my playthroughs I've completely ignored the MQ; one of which I've gained access to Whiterun, the other I've completely ignored it. Hell, on my second playthrough I even ignored the Helgen attack. I only played through it as a formality as it wasn't part of the story for that character