Okay so on my newest character, I made the decision to not progress on the main quest line to the point where I remain free from random dragon encounters.
However, I'm trying to complete the Civil war quest line. I'm at the point where I've given Ulfics War axe to the Jarl in Whiterun, however, he refuses to make an decision until the dragon situation is sorted.
But if I sort said situation, that would mean having the random dragon encounters which I don't want.

Is there anything I can do?

You can wait for mods, I suppose. There isn't any way around it if you wish to progress the Civil War questline. There might also be a way to change the main quest stage with console commands though.

You could just not do the civil war quest line untill you are ready for the encounters.

I'm ready for them, I know how to fight them, and I can easily, I just don't want to.
They're too easy, they're far too common, they're just annoying.