When I started low carb I used to keep some of the 20g packs of cheese at the front of the fridge so they were the first thing I saw!
"Low or no carb" rather than foods that T1s on insulin might eat:
most full fat cheeses - try wrapping a lettuce leaf around a slice of cheese
cooked chicken legs
a small quantity of olives or nuts (some nuts are higher in carbs so check the labels)
some cold crispy bacon
eggs - as a change from hard boiled I make eggy 'muffins' with a little double cream and some grated cheese in them, good hot or cold, I add black pepper plus paprika, or chives, or a little soy sauce
a slice of ham
a small amount of full fat real Greek yogurt with 5-6 raspberries stirred in
One square of 85% dark chocolate - again check the labels as some are better, I like the 85% Lindt. You can even make a small hot chocolate drink by stirring a square into hot water with double cream instead of milk.