I'd fess up before trying any DIY cleaning without her knowledge. If the DIY cleanup doesn't go well, it will be orders of magnitude worse. In other words, when in a hole, stop digging!
There's also that chance it really didn't come from your bike. But it does look like it had to brush up against the cassette for that mark. How in the world would that have happened. Unless of course, you are the moron your wife undoubtedly believes your are.
Good luck!