It wasn't a great surprise though, as this is a very noisy instrument.
The compartment cover was just a plastic disc held in place with an ungrounded metal strap. Of course grounding was also poor, with ground loops, potentiometer cans used as ground points, etc.
Although there wasn't any internal shielding (not even conductive paint— I checked with my ohmmeter) the pickup mounts seemed to be designed to work with shielding, since they had grounded copper spring mounts.
There's some decent advice on improving the shielding and grounding in a Stratocaster available at Guitar Nuts here: Quieting the Beast, Shielding a Strat™. I adapted some of the implicit goals of that article to the Dano '63. The most significant differences are related to the relative simplicity of the Dano: Two pickups, single volume & tone, single-pole selector switch with pickups in series. The way a Dano selector works is by shorting out the unused pickup when not in the center "series" position.
I used Copper foil tape with conductive adhesive to shield the electronics compartment, pickguard and back cover. Since the peculiarities of Danelectro body construction leave lots of inaccessible voids, I had to make little foil dams near the controls compartment.
I didn't end up creating a signal ground terminal as described in the article, since there were so few signal grounds to tie together: One from the jack & volume, one from the tone capacitor, one from the pickup selector. I just soldered them together and added some heat-shrink to insulate them from the shields.
I also omitted the large ring terminal under a potentiometer to connect shielding, as the pickup selector switch had a nice solder lug on its shield. I did use ring terminals to attach the bridge wire and pickup shields to the foil shielding.
I ended up replacing the tone capacitor, since the original was soldered onto the back of the potentiometer and had its leads cut too short to b
e usable in any other configuration. The new tone capacitor as well as the new 0.33μF coupling between ground ans shield are affixed with double-face foam tape.