One option for both would be to make (or buy) a router trammel which
would give the router a pivot point.

I would make a template for the interior hole by using the trammel for
the corners connecting them with straight cuts as required. Use the
template as a guide for a pattern bit to cut the actual interior hole.
Make the template large enough to get a couple of clamps on it that
don't interfere with the router.

For the exterior corners, again make a template with the trammel and
use a pattern bit. For these radii cut as much of the corner off with
saw as you can. Make very light cuts with the router. This type of
operation can catch the wood and cause large chip out. That will make
you think bad things.

Suggestion, go buy some 1/2" MDF and keep it around for template stock.
You can buy a lot of MDF for the price of most store bought templates.