The phrase "nobody the wiser" is often used to describe a situation in which a person does something without anyone else noticing or becoming aware. There are several synonyms that can be used in place of this phrase, such as "under the radar," "unnoticed," "sneaky," "clandestine," or "covertly." Each of these words describes an action or situation in which a person is able to accomplish something without drawing attention to themselves. For example, a person might sneak out of a party unnoticed, or they might do something covertly to avoid being caught. Regardless of the exact word used, all of these synonyms convey the idea of getting away with something without anyone else noticing.