|laziness, impatience, and hubris|
Truthfully, I've no idea, but I wasn't thinking about manoeuvering either (except maybe rotating the deflector to be at right angles to the debris path). Just the entire assemble, shuttle'n'all. And I'm not at all sure that the shuttles are capable of remote operations either, though if they're not, they could be made so--for some amount of money.
They already track the debris pretty accurately and can predict their future course sufficient that they can avoid them when planning shuttle launches and manoeuvers, though they probably use wide margins of safety. And they have to be able to position the shuttle pretty accurately for docking, so I don't think control is a problem.
If you imagine the deflector being a 3 cm thick titanium plate that is elliptical, and as large as can fit in the shuttle bay--say 15ft on the minor axis and 30ft on the major, for a weight of about 4 tonnes.
If presented to the debris at a 30deg angle to its path--you have a 15ft diameter target. Many times the tolorance for docking. With military spec GPS guidance that should be possible. It really comes down how accurately the debris trajectories are known.
I think the really major part of such an operation would be planning minimal maneouvering of the shuttle to allow it to intercept the maximum number of pieces without wasting fuel. The shuttle wouldn't have to chase after the debris. Just be in the right place as it comes by.
The bit I really have no feel for is whether, say a camera hitting the plate would cause all the bits to predictably directed in the desired direction, or whether you'd end up with a dozen more pieces of debris on new paths?
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