Water that "burns up" in the atmosphere recondenses and enters the planet's water cycle.

It's the dinosaur-killer effect you're wanting to avoid ... the transmission of a huge amount of energy into the planet's crust, kicking up dust that obscures the sun, and also causing earthquakes & tsunamis.

If you just say all the ice meteors were no larger than the hippie vans, you'd be fine, and you can dump as much water as you like into the system from space.