There are numerous synonyms that can be used in place of the phrase "not touch". Some of these include abstain, avoid, dodge, evade, omit, shun, steer clear of, and keep away from. These words can be used in a variety of contexts, from warning someone not to touch a hot surface to advising someone to stay away from a certain individual or situation. It is important to consider the context in which these words are used, as some may have a negative or positive connotation. Ultimately, these synonyms allow for a more varied use of language and can help to convey a more nuanced message.