In Islam, the fast is not broken by administering any sort of substance in a way that it does not enter the gut system (mouth, esophagus, stomach, intestines, colon, rectum). So, a nicotine patch is fine. Diabetics who require insulin injections are also able to administer this during fasting without issue. But of course, it is better to not do any of these during the actual fast. A person may even smoke after he breaks his fast after sunset if he must (although there is a big difference of opinion on the permissibility of smoking, with some scholars saying it is disliked to others saying it is forbidden so it is still best to avoid it since even the permissibility of it isn't without dislike). Also, using a miswak would be better than a toothpick since it is a major sunnah as well.