Why does Ned Stark only take his older sons (but not Sansa) to watch him execute the deserter?

In the pilot episode of Game of Thrones, Ned Stark takes his sons Robb, Jon Snow, and Bran to watch the execution of a Night's Watch deserter in order to teach them that

The man who passes the sentence should swing the sword.

If either one of Ned's sons were to become Lord of Winterfell or take a leadership position, he would have to execute the criminal that they pass the death sentence to.

But if Sansa became the Lord of Winterfell and had to deal with deserters or other criminals whose crimes deserve capital punishment, would she have to swing the sword herself? Why or why not?