The answers with the meaning are great, but to be more specific, "never" and "no": _scathe_ isn't considered a word and using it as a serious synonym for _injure_ would be confusing.

Because of _unscathed_, _scathe_ is vaguely associated with injury. In "I scathed my hand", scathed jumps out -- "you did what? What's a scathe? No wait, I just had lunch. Don't tell me". In a fantasy book we might assume a scathed hand is a magical injury to be explained later.

Also because of _unscathed_, _scathed_ is a joke word. If you said "2 people were scathed in a car crash", you're making a joke about their injuries (a joke such as: "the driver was unscathed, but the two passengers -- let's just say they were scathed, badly".)

The common phrase _scathing insult_ gives another possible guess. "John is going to scathe you" sounds like made-up teen-age dialogue. He's going to humiliate you, but nothing physical.