Whichever method you use, you'll loose the thickness of the saw kerf
at least in the cut (and on each side of the cutout board). You could
batten the edges after making the cut, in which case you would have
the opportunity to clean up any irregularities.

As John says, plunge cut with a circular saw (riving knife, if there
is one, removed). Practice on a bit of scrap board first, and use a
guide for the cut (especially when starting plunge cuts). It isn't
really that skill demanding, more about having the nerve to do it.
Ensure the start and stop points allow the visible upper curve of the
blade to stop just short of your corners, leaving about an inch on the
underside.

To get tight, square corners with no overcut, you'll then have to
handsaw/jigsaw/multimaster the first and last inch (again with a
guide, unless your skill level is up to it).

It's possible to plunge cut with a jigsaw (very gently tipping back
from the front edge, whilst very slightly moving forward), but that is
somewhat skill demanding.