[papercrane]

A gravity tractor is the simplest solution with enough lead time. It's theoretical, but doesn't involve any exotic technology or materials.

Essentially you have a spacecraft park itself beside an asteroid. It's gravity will minutely change the asteroids trajectory. With enough lead time that's all you need. Since you're not blowing up, or applying a large focused amount of energy to the asteroid it doesn't matter what the targets composition is. You won't break it up.

https://en.wikipedia.org/wiki/Gravity_tractor