If you are going to do that, don't.
A lot of the monitors rely on that frame to hold them together. Some of the parts are mounted in the plastic. Besides, they make a 19" just for this purpose. It has a frame that you just screw into a piece of plywood, no hacking required.
http://www.hollandcomputers.com/productcart/pc/viewPrd.asp?idproduct=6003&idcategory=2071#detailsIt's VGA, and it's resolution is EGA & VGA (1024 x 768). It has a frame you can just mount in to a cutout, and you are done with a 15 pin connector and a generic video card. Plus, it's only $219 shipped. Most games are only CGA, and even the high end games are VGA. This one will even work in a Jamma setup. It's a 4:3 aspect ratio, which to me is better than a 16:9 for video games
Bigger isn't always better. I have played pacman on a 25" monitor, and it's just not right to me. This one will work just like a regular monitor. I've seen this in games, and it's okay. The black level is a little weird, but doable. I never had one myself.
I've bought some multigames from these people, and they stand behind their products and know what they are talking about. Call them and talk to them if you have questions.