an edge in her tone

"She answered with a slight edge in her tone"

¿Respondió con un ligero nerviosismo en el tono de voz?

Correct, MF, if someone is "edgy", he/she is in some way nervous.

hermit

Thanks a lot.

"On edge" is a way of expressing nervousness. (I was on edge because I was waiting for the results of my test.)

Speaking with an edge in your tone might convey tenseness, anger, unfriendliness. The word edge brings to mind hardness, coldness, no forgiveness.

Getting off on a tangent here, but:
Edgy is also used to refer to something/someone that is hip and cool, at the forefront of style.