Blowing out your reflection on the DVD using flash is a viable option, assuming that doesn't also overexpose any details you need to retain/show (labels).
Other options that help are to reduce your reflection by shooting through an opening in a white sheet or similar to create a large/even white reflection... that will still leave the lens element as a ...
Use a flash and 1/200 shutter speed.
The high shutter speed makes anything not lit by the flash unnoticeably dark.
The flash hits the shiny DVD directly, so it doesn't need a lot of power, and thus doesn't backsplash a lot to the camera and photographer. It might also help to pull the camera back a bit and then zoom in a bit, to further deplete the flash's ...
You can easily fix the slanted picture in post-production using the perspective correction tool of any good editor (Gimp, PS...).
Use a remote controller (or a trigger delay) so you aren't next to the camera
Shoot through some makeshift screen (preferably dark) with only the lens showing
Make the camera area very dark (variant/addition: ...