Many have tabs on the corners that you can bolt right through and are designed to hold the wait of the monitor.
For example, this 21" monitor in my cocktail cab:

is suspended underneath by the four corners only:

Also,, if you pay attention to your disassembly and are careful, you can just put it all back together again if things don't go your way.
Now, for my upright, I didn't decase, but I did paint the beige plastic black and built a bezel:
