I used to take the contents of sandwiches out to eat and throw the bread away if there was nothing else suitable to eat - ham, cheese, tuna, salad extracted with a spoon or fingers. You could even eat the inside of a sausage roll although the cheap sausage filling does include carb heavy binders.
Take hard boiled eggs, pieces of cheese, a tub of salad, a tin of tuna, etc.
I wouldn't advise taking meat or fish unless you have a cool box or can put it somewhere cool. If you can then roasted chicken legs are good.