As old_tv_nut says, the best solution is to do a double exposure with a still image on the TV and your camera mounted on a firm tripod.
For the first exposure, you have the TV turned off and lighting arranged for best display of the cabinet. For the second, you turn on the TV -- without moving the camera! -- and adjust the lighting (often very different) for best display on the CRT.
You later copy and paste the CRT image into the TV cabinet image, using a program such as Photoshop, Paintshop Pro, etc. You can see a nice example of this at:
http://www.radiolaguy.com/images/Admiral20X11pix.jpg
As I have learned from experience, it's fiendishly difficult to take a good live picture that accurately represents both the cabinet and the screen. If the cabinet looks good, the picture may be too bright or too dim, or too blue in the case of b/w TVs. If you adjust to get a good screen shot, the cabinet will be too dark, and so on.
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html