Sounds like quite the challenge!
I understand from your post that you won't have any fridge, but you WILL have 2 pots, a frying pan, and cooking capability?
IF so, you have some great choices. My DH bicycled across Canada a couple of summers ago (the ultimate in no fridge!) and lived to tell the tale, and you will too!
You might want to bring a backpack dedicated to a kitchen pantry.
Spice and herb collection: chili powder, curry powder, italian seasoning mix, salt, pepper
Rice, pasta, couscous
Tinned black beans, kidney beans
Tinned tomatoes (whole, diced, or ground aka "passata")
Pita bread, whole grain breads
Peanut butter, jam, marmalade
Texturized Vegetable Protein (dry soya, essentially, for protein)
Tinned Tuna, Tinned Salmon, Tinned Chicken
Salad dressings, fat-free and in spray-pump bottles
Fresh veg and fruit
Fresh meats if eaten that day
Eggs, if eaten pretty quickly
SMALL tetrapacks of milk (cow's or soya)
Tea (of course)
Some meal suggestions:
Instant Oatmeal (boiling water) and fresh fruit with milk
Tea, multigrain bread, marmalade or jam
Tea, multigrain bread, peanut butter
Eggs (egg white omelet, scrambled eggs, boiled eggs)
Tuna or Salmon or Chicken and rice with fresh veggies
Vegetarian Chili made with Texturized Vegetable Protein (aka TVP), tinned tomatoes, tinned beans, spices, served with or without rice
Pasta with tomato sauce, bulked up with mushrooms (you can even bring tinned mushrooms if you like!) and other fresh veggies
Pita with fresh veggies and black beans
Well, you get the idea. Just rinse the tinned stuff really really well to minimize the salt action, and get everything packed in water...And use fresh if possible (i.e. fresh tomatoes is ideal, but tinned ones will be just fine...)
I AM, of course, assuming that you have access to cooking, hence the two pots and frypan...