The right way to do it is what works best for you. Your proposed method is fine, and I'd use a jeweler's saw to cut out the panel. If you don't have a jeweler's saw, a jigsaw with the finest blade you can find may work. This is what I do.
It is generally better to cut well within (say 1/16 inch to 1/32 inch) within the ultimate opening, and then carve or file the final borders, as files and small knives are easier to control.
You can also scribe through, but I find that tedious, and the knife always slips at the worst possible time, leaving me a repair job, too.
If you have a motor tool with the right bits and speed control, you can grind it out with cutting burrs. But remember that power tools allow you to screw up a project far faster and more efficiently than you could ever manage by hand…
@#!#&*#$%!!!