I didn't have a pee-ing problem with the carriers. With one cat (Mister, rip) he would have a screaming, yowling, howling, hissing, growling fit complete with acrobatics. A scruff hold did nothing, just gave you a handle to hold him by. His mouth was making all kinds of racket and his teeth and claws were like ninjas in a fury.
It go to where we had to wrap him in a towel and stuff him in the carrier to protect ourselves. After we moved to GA, he would get curious about a carrier brought inside so I would place it on the floor and when he came near the opening, I'd open it. When he walked in, I'd quietly close it.
Eventually, he got wise to that and stopped going in.
For the last few years of his life, I would put a harness/leash on him and he did just fine.
I would recommend wrappingkitty in a towel (completely, so she can't see where she is going) and placing her in a carrier. Leave the towel with her, if she pees, the towel will soak it up.