Both of ours would just eat packet food if we had it in until it was gone.
So if they want to eat after school, before dinner, they of course have snacks but they are limited choices and this list isn't a menu of what's on offer each day just examples
Crumpets with marmite and tahini
Hard boiled eggs
Greek yogurt with blueberries, honey if I am feeling nice
Glass of full fat milk
Occasionally I am super nice and heat them frozen sausage rolls
Falafel dipped in houmous
Apples
Left over home made desserts - but a controlled portion
Oatcakes
They might resort to toast but as a rule if there was dinner to follow they wouldn't have the option of cheese
They quite like the fish paste jars you can get, salmon is their favourite but you can get crab, sardine and tomato - they are ok on toast with cucumber
Bit of french bread stick with houmous
breadsticks
Plain nuts, like the ones you crack occasionally
What I don't buy as a general rule, biscuits, crips, anything you can put in a microwave - think those burger things, we don't always have a microwave regardless and it's a bit hypocritical as I lived of microchips at their ages (but they don't know that), chocolate, single portion anything, bakery items like donuts well I might but we are talking once a month.
If ours were eating too much cheese I wouldn't have much in the fridge, I would buy smaller blocks on the day you want cheese with something. Yes it's more expensive but if you want to get their raiding the fridge and cupboard for unhealthy calorie heavy food it's easiest if you remove or fully control what it is they go for.