A jig saw can do that, especially if you test various blades to find the right one .
(Or the right Jig saw, not all are the same)
But finish is not so good.If it is not visible, I'd go for that quick way .
The portable router can do it better, except corners.
I would use the cutter I' v got in a standard set of cutters:
Straight bit with a bearing at end of cutter, diameter not critical like 1/2 " is good.
First thing is to make a jig out of some 1/2 or more MDF, that would be exactly the
aperture you want to make.Use a Jig-saw, a file, some putty if necessary.
This shape will be copied by the bearing.( Copied with any errors)
The jig saw be used to clear the way, cut the inside of your fabrication, leaving around 1/8 " or less to be cut.
Apply jig exactly on the lines to be cut.
Set depth so that bearing will contact jig, and that cutter would cut your part.
cut from your part side at set depth , going against the cut that is clockwise inside the hole.
There still will be some work in the corners, that will have radius 1/2 dia of the cutter like 1/4 " for a 1/2" cutter.
Thats a way to do it, there are other, like cutting directly through your material, using a router compass attachment
a standard straight bit and some geometry,
but I would not, it seems difficult and with risks of mistakes.0
Or if material is cheap, maybe Yes.