Do the testing to figure out how to change their orbits on asteroids who’s orbits are now entirely inside ours. Minimize the risk. Once you’ve figured out how to move them then do the additional work to determine how to approach asteroids in potentially dangerous orbits to apply the lessons of the former.
It really isn't that hard to understand. Conservation of momentum still works.
The unknowns are what happens 100-200 and more orbits from now when a close encounter now could become a direct hit then. The big uncertainty comes in that small changes in closest approach now can produce dramatic changes in future orbits.
Actually doing it is a big deal, but understanding how an impactor would work is not that hard.