Yes, your mixture is basically correct: roughly 75% KNO₃ with the remainder charcoal and sulphur. Charcoal was usually in excess but compositions vary. Blasting powder for mining and quarrying has less nitrate. Sodium nitrate can be used and is as powerful, but is hygroscopic and therefore deteriorates faster unless kept sealed. However, du Pont manufactured a low-sodium nitrate form where the grains were coated in charcoal yto keep them dry, this was only for quarrying.