What exactly is your reasoning for choosing a customer service job? If you stutter more when you’re on the phone do you think you would be happy in a job that requires phone conversations all day long? Or would you be able to provide customer service through a chat mode online? If it’s all telephone customer service it may or may not be a good fit, but if it’s online in a chat format, or through email it might be easier. You may want to learn more about the jobs to see if they would be a good fit for you.