Her actions in Skin Game are why I'm suspicious, specifically because of her mental state in Ghost Story and Cold Days. I dunno - maybe she did a lot of healing since Cold Days. But she went from being frightened that Harry would fall to being dead certain that he would not despite evidence to the contrary, went from not wanting a relationship with Dresden to falling all over him, and went from being very internally troubled and conflicted to being the sudden voice of reason. I dunno, it's certainly possible. And I do agree - if you take what she says at face value, she'd never be a traitor, ever.
The events of Cold Days explain the change. Karrin is wary of Harry, yes -- when he first comes back from the dead and she hasn't seen him in a year.
Then he spends the whole book being Harry. In that, she sees that he's not the monster he or she feared he is. He has some, shall we say, growing pains to deal with as far as the Mantle goes, but he proves repeatedly throughout the book that he is still Harry Dresden.
Seriously, just because Murphy's opening dialogues with Dresden in the book have her wary doesn't mean she's that way the whole book. She doesn't exactly push him away when he promises to do things to her that will have the neighbors complaining.
I'd suggest rereading Cold Days. She's the "voice of reason" to Harry himself there in a few places, and the things you're describing as a change between CD and SG are things that were present in CD in the first place.
By the way, what I was referencing was how she attacked Nick with the sword, despite Harry telling her not to. She could have shot him. She could have attacked Big, Tall and Stinky. She could have called his bluff. But instead she chose to go the route that would have ensured the sword's destruction and Harry's or Michael's death, completely sabotaging the mission, all because she listened to her fears and did what felt was the only thing she could do at the time to protect him.
Harry was the one who asked her if she was going to bring the Sword in the first place, and suggested she should bring it along.
Attacking Big, Tall and Stinky exposes her back to Nicodemus, at which point, hey, she's dead before she makes it to the big guy. Plus, the big guy is holding Harry in his hand. That's going to make it next to impossible for her to strike him effectively, and if she attacks him, there is nothing stopping him from just casually crushing Harry anyway.
Shooting Nicodemus does nothing, as we've seen numerous times before. The last time we saw him shot with anything less than an AK, his reaction was literally to roll his hand with a "get on with it" gesture because the only thing the gunshots did was muss his outfit.
Calling a hostage-taker's bluff is among the least intelligent things to do in a hostage situation.
And besides, it wasn't a bluff. Nicodemus might say it was a "ploy," but he outright admits that he wasn't sure if the Sword was in play. You can't say the entire thing was a ploy if the one thing it's supposedly a ploy for might not even be there. Saying it was a ploy is Nicodemus's excuse, and he explicitly likens it to the fiction that Harry really was pursuing Butters.
Which is to say it was bullshit, pure and simple. Nicodemus absolutely would have killed Harry and used Harry's own breaking of the agreement as justification if Murphy hadn't stepped in.
Seriously, what exactly is the sequence of events if Murphy doesn't act? Do you really think Nicodemus is going to go, "Oh, nevermind, put Harry down, let's get on with business"?
As I recall, Harry doesn't tell her not to attack Nicodemus with the Sword. He tries to tell her not to execute him with the Sword, but that's only after she's won their initial exchange.
Really, if you want to look at someone "completely sabotaging" the mission, that person's name is Waldo Butters. Without him acting on his misplaced fears -- and outright rejecting the things Murphy herself told him about how they can trust Dresden -- Karrin would not have been put into a situation in which there were no good options.
She ended up against an opponent that was out of her weight class, and who was able to outmaneuver her, and she lost badly. That is by no means the same thing as "completely sabotaging" the mission.