Chemical herbicides are very poisonous, and contain many known carcinogens and other toxic ingredients. Before chemicals herbicides were used in such a widespread fashion, natural and organic controls were used. Mechanical control including pulling weeds by hand was used to control weeds.
One way to selectively control weeds, especially those growing in cracks and rocks, is the use of vinegar and water. The solution is sprayed on individual weeds and has a definite effect in just a couple of days. Heres what you will need:

Create a mixture that is 1part vinegar and 2 parts water. Put the mixture into a spray bottle and shake. Mixture works well for weeds in between cracks on sidewalks, may kill grass if used on your lawn, so try it on a little patch before moving forward with such applications.

"Sidewalk cracks with weeds
before spraying with vinegar"