The Federation may not believe in capital punishment but the Female Changeling was basically Hitler for the Cardassians and she was responsible for all Starfleet, Klingon and Romulan deaths during the war. I don't see how she can walk away from that.
She isn't walking away. She's going to prison. Who do you think is going to execute her?
The Federation doesn't execute people. They didn't execute any Maquis. They didn't execute Khan. They didn't execute Dukat. They actually allied themselves with Damar. They will even actively try to save their enemies' lives in some situations (if they can do so without risking themselves).
The Romulans wouldn't want her executed, either, they'd be far more interested in her being interrogated for information about the Gamma Quadrant. Which could be a diplomatic issue if the Romulans decided the Federation wasn't interrogating her hard enough or sharing enough info, but it wouldn't lead to any calls for execution.
And as far as the Klingons are concerned, a good death is the highest honor. Now, if she were the changeling who impersonated General Martok, that might be worth an execution. But she was just an enemy general, doing what every general does. It was probably 'dishonorable' of her to surrender alive, but the Klingons are more than used to accepting the Federation's habit of taking prisoners even if they prefer not to themselves. There's no reason whatsoever for them to push for her execution.
The only people who would actually push for it would be the Cardassians, and exactly how much influence do you think they'll really have, considering it was their jingoistic alliance that allowed the Female Changeling to wreak havok in the first place?