The phrase "cautious bite" can imply a sense of hesitancy or restraint when biting into something. Synonyms for this phrase might include "tentative nibble," "guarded munch," or "careful chew." Other options could be "timid taste," "hesitant sample," or "guarded try." These alternatives capture the sense of treading carefully and being mindful when engaging with the object being bitten. Additionally, synonyms such as "moderate gnaw," "gradual chomp," or "deliberate nibble" could also convey a similar connotation of careful consideration and measured action. Ultimately, the choice of synonym will depend on the context and the tone the writer wishes to convey.