You have a GE box, not a Bulldog. You should be able to get a couple of 20 amp breakers at any Home Supply store.
The instructions above for making a new shore cable are excellent. However, you should keep the ground separate from the neutral white wires. The way it is connected now is the original method, with the ground wire bonded to the metal box. The original outlets were ungrounded.
It would be a good idea to add grounded outlets if you can. Current code requires a separate ground wire, but 1959
rules allowed grounding through the chassis.
If you like, you could add a separate grounding bar where the ground wire is now screwed directly to the box.
The green wire that comes from the light socket is supposed to tell you if you have a "hot neutral". The green wire should go to ground; if you have a hot neutral, current will flow to ground a the light will tell you you have a problem.
If you have only two breakers you do not need a main disconnect and main breaker.
Here's a picture of a Bulldog box.