In theory, nitrite could be omitted if the pH of the meat was lowered with a lot of citric acid to less than 3.8 (minimum pH for Salmonella). The sausage would have the sourness of a lemon.
It is used in commerical salami because it immediately decreases the pH vs. natural fermentation that slowly produces lactic acid. To actually do this experiment in a rigorous way, one would add the citric acid then challenge the meat with pathogenic bacteria (salmonella, cl. botulinum, staph., campylobacter, listeria, e. coli, shigella, and bacillus) and look at their survival. This would require a lot of containment and specialized equipment. A badly done experiment would be to add citric acid, eat the sausage, survive (?), then claim that it always works. I would suggest a science experiment for your daughter would be to measure the pH of various salami and have them rated for sourness.
Fashionably late will be stylishly hungry.