I dunno, I think that even a small bit of metal hitting the shuttle during re entry would be more than sufficient. Look what a piece of foam did.
Keep in mind, as has been mentioned, the thing cant evade.
At the speeds coming in, if you can create enough disturbance (either a shockwave or damage to control surface) to make it loose control even slightly odds are pretty good you’d cause a crash. No way it would be able to recover from 2 to 3 miles from landing.
As for hitting it, I still think that it should be possible to set up a targeting solution where the shuttle more or less hits the rocket. That is, you set up a solution that puts the rocket and the shuttle in the same place. Again, you have the pertinent information to do this and its not like it would take a powerful computer to calculate. Heck you could probably set up some automated computer controlled frame to fire the thing if you really wanted to be fancy. (Although I still think that a couple dudes firing at the same time would work better).
Oh wait… just thoguht of something… at the ranges that a man portable missle operates (so, what was it, 2-3 miles from surface?) what speed is the Shuttle travelling at? Cause if it’s slowed down enough then my theory gets shot to hell.