"Likely to go off at half cock" is an idiomatic expression used to describe someone who is impulsive or rash in their actions. Synonyms for this phrase could include "hot-headed," "impetuous," "reckless," "hasty," "thoughtless," or "trigger-happy." All of these words convey the idea that the person in question is prone to acting without considering the consequences, and could potentially cause harm or damage as a result. It's important to be aware of these tendencies in oneself and others, and to strive for a more measured and thoughtful approach in all situations.