I am curious, without ANY sugar, do you also mean sugar substitutes, Splenda, Xylitol etc.. or any fruit... and what about fruity vegetables (carrots etc).
We eat a relatively low added sugar diet and have these snacks: Nuts, rice cakes, nut butter (1-2g of sugar per 100g), seeds, roasted chick peas, pop corn, vegetables with humous, tuna mayo dip, crackers and salami. pancakes with dried meat.
Using dates to sweeten.... (these are also dairy and gluten free but you can adapt the recipes..).
Sweet potato brownies (200g of sweet potato, 100g of date paste, 1 tablespoon of cocnut oil, 3 eggs, 3 tablespoon of cacao powder, vanilla powder). Mix the dates, coconut oil and sweet potato in a blender then add the eggs, beaten in by hand.
Banana bread: 100g gound nuts, 200g bananas, 2 eggs, 50g raisins.
Almond biscuits 100g dates, 100g almond butter 1 egg, spices to taste.
Ice cream: Frozen bananas and frozn fruit.
HTH