Mm, I don't see how that will minimize fighting. Mages are defending themselves regardless in either situation -- I dare say that with the Champion on their side they won't feel as hopeless and are more likely to keep a clear head. Because they aren't alone. There will be damage no matter what.
Siding with Meredith just because "it's inevitable" is part of the problem. Genocide isn't the answer. Protecting the Circle is protecting innocents, and that seems well within what a Champion would do. Saying "this is a bad thing that I can't stop so I'll go along with it anyway" when you actually have a choice to fight it. "The only way bad men win is when good men do nothing."
What you are doing is reducing the issue at hand to a simple moral conundrum. The Circle is innocent of what Anders did, ergo protecting it is protecting is innocents and that is good.
However, there are other factors to take into account such as the civilian population of Kirkwall and how they are affected by the fighting.
The number of Templar combatants are more numerous that the mage combatants given the fact they don't have a civilian population. Likewise, the mages are a minority when compared to the kirkwallers.
Let's say that there are 100 combat ready mages against 300 templars with a thousand civillians in the middle.
Whoever has Hawke assisting can kill 25 enemies per round with 50 civillians dying per round as well.
So, if Hawke sides with the mages, it will take 12 rounds to defeat the templars which leads to the death of 600 innocent civilians. You've killed six innocent people for every mage you saved.
On the other hand, if Hawke sides with the templars, it will take only four rounds to defeat them all which means that only 200 civillians die. That is a difference of 400 innocent people which is four times the number of the mages.
Logically; despite the fact these numbers aren't exact; we can see that siding with the templars saves more innocent lives than siding with the mages.
Then, there is also the fact that eliminating the mage population will eliminate the reason for contention within the city whereas saving them will not. By eliminating the reason for conflict, we eliminate it thus saving even more lives.
Now, this involves killing innocent people, yes but to save even more.
And again: protecting mages it what templars are supposed to do. We'll probably never agree on this subject because I don't see how genocide solves any problem. (Unless it's about Aliens... Then I might agree.
) Moreover, this incident would only spread to the other Circles and a rebellion would still be inspired. Crap already hit the fan. Game over. Siding with Meredith just places Hawke on the wrong side of history.
The "wrong side of history"?
C'mon now, that is a very complex subject that involves victorious factions spreading notions that become widely accepted by the population at large.
Suffice it to say, the mages don't meet any of these requirements. Even in the event that the Inquisition sides with them, there is never any indication that the population has accepted a pro-mage narrative regarding the incident in kirkwall and before the DAI, the mage rebellion was despised by everyone in Thedas with every city except Redcliff barring their doors to mages.