The dictionary definition of shunt that applies here is it means "allow movement".
Timestream refers to personal history. Generally it gets used in Doctor Who in multiple Doctor specials where each Doctor is considered to have his own timestream.
Basically Doctor Who is paradox free except for the personal history of a time traveler. See the 9th Doctor episode Father's Day. Where the 9th Doctor changed his own history and a hole ripped in the universe.
For the rest of us the details of events are constantly drifting in the details with some things being fixed. So The Doctor can step on a butterfly in the past and it won't particularly change anything that wasn't going to be changed by drift anyway. That's why observing time was a full time job for Gallifrey because history is always changing for the rest of the universe.
Amy is pointing out they can't fix the duplicate Amy problem without causing a paradox that would require a serious amount of effort to maintain. A TARDIS can do something like that maybe but it's a full time effort. The Master, for example, converted the TARDIS into a paradox machine when he wiped out humanity with the converted humans Troclafane from year 100 trillion. Time snapped back when it stopped supporting the paradox.
Though this may be a lie by the Doctor- a TARDIS can maintain a paradox - but it is a bad idea.
Also from this episode (a second use of shunt):
Perhaps, maybe, if I shunted the reality compensators on the TARDIS, re-calibrated the doomsday bumpers and jettisoned the karaoke bar, yes, maybe, yes. It could do it. The TARDIS could sustain the paradox.