Built in '56?
Is the electrical service actually up to date behind the drywall?
Original drywall?
Depending on the quality of the finish on the interior side of the exterior walls, I'd at least consider stripping the drywall and rewiring/insulating/drywalling with new.
In a house of '56 vintage, a house with no insulation might very well have been built in an area where code didn't require fireblocking yet, so you ought to have that installed.
If your fire code was up to date in your area in 1956, you ought have fire blocking by code in the walls which would mean that you can't just open the top of the wall and insert insulation by blow-in or foam.
One issue with the blow-in -> It settles (as much as 25%) over time, leaving gaps at the top of the walls with no insulation.
If you have fire blocking you have to blow it in at ceiling and at approx 4 feet above the floor.
Both methods require patching all the holes, and you're still stuck with 1956 wiring and fewer outlets, no cable/ethernet, etc.
Nothing is black and white, nothing is easy.