There...might be a way to bypass a large portion of it. You'll still have to do some fighting, but not nearly as much. I will warn you now, though, that I have no idea if this will actually work.
The key is simple: Master Stealth. If you're not a Rogue yourself (or you are, but don't have Master Stealth), then you'll need to bring Zevran with you. If you killed him, you're ****e out of luck.
Now, when you enter Caridin's Cross, take control of the rogue. Put the rest of the party on hold, then activate Stealth. Now, make your way straight to the exit leading to Ortan Thaig. Go ahead and leave normally, and your party will be transported with you to Ortan Thaig.
When you get to Ortan Thaig, do the same thing: put your party on hold, Stealth your Rogue, then make your way forward while avoiding any fights. The tricky part is that you need to fight the Corrupted Spider Queen. Now, just before the bridge, release your party from Hold. Because they are off the edge of the mini-map, instead of having them run to you, the game will instead teleport them to your side. You can then go in and kill the few enemies here, take on the Corrupted Spider Queen, then read Branka's Journal and leave.
In the Dead Trenches, you can do the same thing: put everyone on hold, send your Rogue through, and travel under stealth. The only thing I can think of that will give you trouble is the Ancient Darkspawn in one of the tunnels; he's an Elite Boss, so he's going to have a very high Detection Rank, so he might detect you. In that case, you will have a fight on your hands.
Continue forward to the Broodmother, who you will, quite obviously, have to defeat. Do so, then head to the Anvil of the Void. You'll have to fight your way through here normally, unfortunately, but considering how much time and effort you saved on the way here, that shouldn't be too hard.
Again, I'm not entirely sure this strategy will work; it was made based entirely on my observations on Leliana's behavior on my Nightmare 'Solo' run with a Dual Wield Warrior (I did all the work and damage; Leliana stayed Stealthed and only picked locks). It's a bit of an iffy proposition, I suppose, but it's the best I can offer.