When we 'fight shy of something', we tend to avoid engaging with it due to a sense of reluctance, hesitation, or apprehension. We may feel unsure about the potential outcome, or we may have reservations about the consequences of our actions. However, there are many other ways to express this reluctance, using various synonyms. For instance, we may use terms such as 'shun', 'eschew', 'evade', 'abstain from', 'refrain from', 'dodge', or even 'keep away from'. Each of these synonyms expresses a slightly different nuance of reluctance, but they all convey a sense of hesitancy and apprehension when facing a particular situation.