You can deffo manage a weekend without a fridge! Assuming you're using a gas stove?
Anything tinned/jar - soup, meat (stew, mince, meatballs, chilli), beans, pasta sauce
Fresh (that should be good until Saturday morning at least) if you buy Friday afternoon - bacon, sausage, fresh pasta, mixed veg for stir fry, hard cheese, salami etc, bread
Basics - eggs (101 uses), packet rices/noodles, crackers, biscuits, cakes
Drinks - uht milk if you really can't live without tea/coffee, squash, juices, beer, wine..
I'd see this as actually quite liberating and not having to conform to normal meal requirements.
(if you must invest in a cool box then take most things frozen - cartons of juice, pre-made spag bol, milk in 1pt cartons (or get the ones from Macdonalds for smaller portions)
Live a bit OP, mini rolls and Ribena for breakfast if you wish!!